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CONTENTS. 


CHAPTER  I. 

PAGE 

Gunpowders 2 

Definitions,  1.  History,  2.  Charcoal  powders,  4.  Smokeless  pow- 
ders, 5.  Guncotton,  6.  Nitroglycerine  small-arm  powder,  7.  Manu- 
facture of  nitrocellulose  powder,  9.  Other  smokeless  powders,  10. 
Proof  of  powders,  11.  Advantages  of  smokeless  powder,  12.  Pow- 
der charges,  14.  Blank  charges,  15. 

COMBUSTION  OF  POWDER  UNDER  CONSTANT  PRESSURE,  16.  Constants 
of  form  of  powder  grains,  18.  Emission  of  gas  by  grains  of  different 
forms,  24.  Considerations  as  to  best  form  of  grain,  27. 

VARIOUS  DETERMINATIONS,  28.  The  number  of  grains  in  a  pound,  28. 
The  dimensions  of  irregular  grains,  28.  Comparison  of  surfaces,  28. 
Density  of  gunpowder,  29. 

CHAPTER  II. 
Measurement  of  Velocities  and  Pressures 32 

Measurement  of  velocity,  32.  Le  Boulenge  chronograph,  32.  Measure- 
ment of  very  small  intervals  of  time,  40.  Schultz  chronoscope,  41. 
Sebert  velocimeter,  42.  Methods  of  measuring  interior  velocities,  43. 
Measurement  of  pressures,  44.  Initial  compression,  45.  Small-arm 
pressure  barrel,  45.  The  micrometer  caliper,  46.  Dynamic  method, 
of  measuring  pressures,  46.  Comparison  of  the  two  methods,  47. 

CHAPTER  III. 
Interior  Ballistics 49 

Scope,  49.  Investigations,  49.  Gravimetric  density  of  powder,  52. 
Density  of  loading,  53.  Reduced  length  of  powder  chamber,  55. 
Reduced  length  of  initial  air  space,  55.  Problems,  56. 

PROPERTIES  OF  PERFECT  GASES,  57.  Mariotte's  law,  57.  Gay  Lussac's 
law,  58.  Characteristic  equation  of  the  gaseous  state,  58.  Prob- 
lems, 60.  Thermal  unit,  61.  Specific  heat,  62.  Relations  between 
heat  and  work  in  the  expansion  of  gases,  63.  Isothermal  expansion, 
65.  Adiabatic  expansion,  65. 

NOBLE  AND  ABEL'S  EXPERIMENTS,  67.  Apparatus,  67.  Results  of  the 
experiments,  68.  Relation  between  pressure  and  density  of  load- 


CONTEXTS. 

ing,  69.  Temperature  of  explosion,  70.  Relations  between  volume 
and  pressure  in  the  gun,  71.  Theoretical  work  of  gunpowder,  73. 

FORMULAS  FOR  VELOCITIES  AND  PRESSURES  IN  THE  GUN,  74.  Prin- 
ciple of  the  covolume,  75.  Differential  equation  of  the  motion  of  a 
projectile  in  a  gun,  76.  Dissociation  of  gases,  78.  Ingall's  formulas, 
79.  Combustion  under  variable  pressure,  82.  Velocity  of  the  pro- 
jectile while  the  powder  is  burning,  85.  Velocity  after  the  powder 
is  burned,  85.  Pressures,  87.  Values  of  the  constants  in  the  equa- 
tions, 90.  The  force  coefficient,  93.  Values  of  the  X  functions,  94. 
Interpolation,  using  second  differences,  95.  Characteristics  of  a 
powder,  97. 

APPLICATION  OF  THE  FORMULAS,  97. 

DETERMINATIONS  FROM  MEASURED  INTERIOR  WELOCITIES,  102.  Prob- 
lem 1,  102.  Problem  2,  113.  The  action  of  different  powders,  117. 
Quick  and  slow  powders,  120.  Effects  of  the  powder  on  the  design 
of  a  gun,  121. 

DETERMINATIONS  FROM  A  MEASURED  MUZZLE  VELOCITY  AND  MAXIMUM 
PRESSURE,  122.  Problem  3,  122.  The  force  coefficient,  131.  Prob- 
lem 4,  132. 

TABLE  OF  UNITED  STATES  ARMY  CANNON,  135. 


CHAPTER  IV. 
Explosives 136 

Effects  of  explosion,  136.  Orders  of  explosion,  137.  Vielle's  classifi- 
cation of  nitrocelluloses,  138.  Conditions  that  influence  explosion, 
139.  Uses  of  different  explosives,  "140.  Bursting  charges  in  projec- 
tiles, 141.  Exploders,  143.  Explosion  by  influence,  144. 

THEORETICAL  DETERMINATION  OF  THE  RESULTS  FROM  EXPLOSIONS,  145. 
Specific  heats  of  gases,  145.  Specific  volumes  of  gases,  146.  Classi- 
fication of  gases',  147.  Quantity  of  heat,  147.  Heats  of  formation, 
148.  Quantity  of  heat  at  constant  pressure,  149.  Quantity  of  heat 
at  constant  volume,  151.  Potential,  154.  Volume  of  gases,  154. 
Temperature  of  explosion,  155.  Pressure  in  a  closed  chamber,  157. 
Complete  calculation  of  the  effects  of  explosion,  161. 

CHAPTER  V. 
Metals  Used  in  Ordnance  Construction 163 

Stress  and  strain,  163.  Physical  qualities  of  metals,  163.  Strength  of 
metals,  164.  Testing  machine,  166.  Copper,  brass,  bronze,  167. 
Iron  and  steel,-  167.  Hardening  and  tempering  steel,  109.  Anneal- 
ing, 174.  Uses,  175.  Gun  steel,  175. 

MANUFACTURE  OF  STEEL  FORCINGS  FOR  GUNS,  176.  Open  hearth 
process,  176.  Other  processes,  180.  Casting,  180.  Defects  in  in- 
gots, 181.  Whitworth's  process  of  fluid  compression,  181.  Processes 
after  casting,  183.  Strength  of  parts  of  the  gun,  187. 


CONTENTS.  XI 

CHAPTER  VI. 
Guns 188 

ELASTIC  STRENGTH  OF  GUNS,  188.  The  elasticity  of  metals,  188. 
Hooke's  law,  188.  Equations  of  relation  between  stress  and  strain, 
190.  Problems,  190.  Stresses  and  strains  in  a  closed  cylinder,  191. 
Lame's  laws,  192.  Basic  principle  of  gun  construction,  195.  Sim- 
plification of  the  formulas  of  gun  construction,  196.  Stresses  in  a 
simple  cylinder,  198.  Limiting  interior  pressures,  202.  Graphic 
representation,  204.  Limiting  exterior  pressure,  205.  Thickness  of 
cylinder,  206.  Longitudinal  strength,  206.  Problems,  207.  Com- 
pound cylinder,  Built-up  guns,  208.  System  composed  of  two 
cylinders,  209.  Application  of  formulas  to  outer  cylinders,  210. 
System  in  action,  212.  System  at  rest,  213.  Graphic  representa- 
tion, 215.  Shrinkage,  217.  Radial  compression  of  the  tube,  219. 
Prescribed  shrinkage,  220.  Application  of  the  formulas,  220.  Prob- 
lems, 222.  Curves  of  stress  in  section,  227.  Systems  composed  of 
three  and  four  cylinders,  229.  Minimum  number  of  cylinders  for 
maximum  resistance,  230.  Graphic  construction,  three  cylinders,  230. 
Wire  wound  guns,  234. 

CONSTRUCTION  OF  GUNS,  236.  General  characteristics,  236.  Opera- 
tions in  manufacture,  239.  Gun  lathe,  240.  Boring  and  turning 
mill,  241.  Assembling,  242.  Rifling  the  bore,  244. 

MEASUREMENTS,  245.  Necessity  of  accurate  measurements,  245.  Ver- 
nier caliper,  245.  Measuring  points,  246.  The  star  gage,  247. 
Calipers,  248.  Standard  comparator,  249. 

RIFLING,  250.  Twist,  250.  Increasing  twist,  251.  Equation  of  the 
developed  curve  of  the  rifling,  251.  Problems,  252.  Service  rifling, 
254. 

BREECH  MECHANISM,  255.  General,  characteristics,  255.  Slotted 
screw  breech  mechanism,  256.  Bofors  breech  mechanism,  258.  The 
Welin  breech  block,  259.  Obturation,  260.  The  De  Bauge  obtura- 
tor, 260.  The  Freyre  obturator,  262.  Firing  mechanism,  263.  Slid- 
ing wedge  breech  mechanism,  265.  Older  forms  of  breech  mechan- 
ism, 266.  12-inch  mortar  breech  mechanism,  268.  Automatic  and 
semi-automatic  breech  mechanisms,  269. 

CHAPTER  VII. 
Recoil  and  Recoil  Brakes 274 

Stresses  on  the  gun  carriage,  274.  Velocity  of  free  recoil,  274.  Deter- 
mination of  the  circumstances  of  free  recoil,  276.  Retarded  recoil, 
279.  Recoil  brakes,  280.  Hydraulic  brake  with  variable  orifice,  281. 
Total  resistance  to  recoil,  281.  Values  of  the  total  and  partial 
resistances,  and  velocities  of  recoil,  283.  Resistance  of  the  hy- 
draulic brake,  Pressure  in  the  cylinder,  286.  Relation  between  the 
pressure,  area  of  orifice,  and  velocity  of  recoil,  286.  Brake  with 
variable  pressure,  288.  Constant  pressure,  288.  Brake  with  con- 


Xll  CONTENTS. 

stant  pressure,  289.  Profile  of  the  throttling  bar,  290.  Neglected 
resistances,  291.  Recoil  system  pf  seacoast  carriages,  291.  Modi- 
fication of  recoil  system,  293.  Wheeled  carriages,  Recoil,  294. 
Design  of  a  field  carriage,  300.  3-inch  field  carriage  recoil  system, 
301.  Recoil  system  of  other  carriages,  303. 


CHAPTER  VIII. 
Artillery  of  the  United  States  Land  Service 304 

Mobile  artillery,  304.  Advantages  of  recent  carriages,  306.  The 
mountain  gun,  307.  Field  artillery,  310.  The  3-inch  field  gun,  311. 
Field  howitzers  and  mortars,  319.  Siege  artillery,  320.  The  4.7-inch 
siege  gun,  321.  The  6-inch  siege  howitzer,  324.  Siege  artillery  in 
present  service,  330.  Seacoast  artillery,  332.  Seacoast  guns,  333. 
Seacoast  gun  mounts,  333.  Pedestal  mounts,  335.  The  balanced 
pillar  mount,  337.  Barbette  carriages  for  the  larger  guns,  339. 
Disappearing  carriages,  341.  12-inch  disappearing  carriage,  model 
1901,  342.  Modification  of  the  recoil  system,  346.  6-inch  experi- 
mental disappearing  carriage,  model  1905,  346.  Seacoast  mortars, 
349.  The  12-inch  mortar  carriage,  model  1896,  350.  The  12-inch 
mortar  carriage,  model  1891,  352.  Subcaliber  tubes,  353.  Drill 
cartridges,  projectiles,  and  powder  charges,  355. 

CHAPTER  IX. 
Exterior  Ballistics 357 

Definitions,  357.  The  motion  of  an  oblong  projectile,  358.  Deter- 
mination of  the  resistance  of  the  air,  360.  Mayevski's  formulas  for 
resistance  of  the  air,  362.  Trajectory  in  air,  Ballistic  formulas,  363. 
The  ballistic  coefficient,  367.  The  functions,  368.  Formulas  for 
the  whole  range,  370.  The  ballistic  elements,  371.  The  rigidity  of 
the  trajectory,  371.  Secondary  functions,  372.  Ballistic  tables,  375. 
Exterior  ballistic  formulas,  376.  Interpolation  in  Table  II,  Double 
interpolation  formulas,  378.  The  solution  of  problems,  380.  Prob- 
lems, 381.  Correction  for  altitude,  383.  The  effect  of  wind,  387. 
The  danger  space,  392.  Method  of  double  position,  393.  The 
danger  range,  396.  Curved  fire,  398.  High  angle  fire,  401.  Calcula- 
tion of  the  coefficient  of  reduction,  410.  Perforation  of  armor,  411. 
Range  tables,  412.  Curvature  of  the  earth,  413. 

ACCURACY  AND  PROBABILITY  OF  FIRE,  413.     Accuracy,  413.     Prob- 
ability of  fire,  415.     Probability  curve,  417.     Probable  zones  and 
rectangles,  420.     Probability  of  hitting  any  area,  420. 
APPENDIX.     THE  USE  OF  TABLE  II,  INGALL'S  BALLISTIC  TABLES 421 

Description  of  Table  II,  421.  Deduction  of  formulas  for  double  inter- 
polation, 422.  Double  interpolation  formulas,  425.  Double  inter- 
polation in  simple  tables,  426.  Use  of  the  formulas,  427. 


CONTENTS.  Xiii 

CHAPTER  X. 
Projectiles 438 

Old  forms  of  projectiles,  438.  Modern  projectiles,  440.  Form  of  pro- 
jectile, 442.  Canister,  443.  Shrapnel,  444.  The  bursting  of  shrap- 
nel, 446.  Shot  and  shell,  448.  Armor  piercing  projectiles,  449. 
Action  of  the  cap,  451.  Deck  piercing  and  torpedo  shell,  454.  Latest 
form  of  base  of  shell,  454.  Shell  tracers,  454.  Hand  grenades,  455. 
Volumes  of  ogival  projectiles,  455.  Weights  of  projectiles,  456. 
Thickness  of  walls,  456.  Sectional  density  of  projectiles,  458. 

MANUFACTURE  OF  PROJECTILES,  460.  Cast  projectiles,  460.  Chilled 
projectiles;  461.  Forged  projectiles,  461.  Requirements  in  manu- 
facture, 462.  Inspection  of  projectiles,  462.  Ballistic  tests,  464. 
The  painting  of  projectiles,  464. 

CHAPTER  XL 
Armor 466 

History,  466.  Harvey  and  Krupp  armor,  467.  Manufacture  of  armor, 
467.  Armor  bolts,  469.  Ballistic  test  of  armor,  471.  Characteristic 
perforations,  471.  Armor  protection  of  ships,  472.  Chilled  cast-iron 
armor,  475.  Gun  shields,  475.  Field  gun  shields,  476. 

CHAPTER  XII. 
Primers  and  Fuses  for  Cannon 477 

Common  friction  primer,  477.  The  service  combination  primer,  478. 
Other  friction  and  electric  primers,  481.  Percussion  primers,  481. 
20-grain  saluting  primer,  483.  110-grain  electric  primer,  484.  Com- 
bination electric  and  percussion  primer,  484.  Igniting  primers,  484. 
Insertion  of  primers  in  cartridge  cases,  485. 

FUSES,  486.  Percussion  fuse,  486.  Point  percussion  fuse,  487.  Base 
percussion  fuses,  489.  Combination  time  and  percussion  fuses,  492. 
Service  combination  fuse,  492.  Combination  fuse,  old  pattern,  495. 
Ehrhardt  combination  fuse,  497.  Detonating  fuses,  498.  The  fuse 
setter,  499.  Arming  resistance  of  fuse  plungers,  501.  Problems,  501. 

CHAPTER  XIII. 
Sights 505 

Principle  and  methods,  505.  Graduation  of  rear  sights,  506.  Correc- 
tion for  drift,  507.  Correction  for  inclination  of  sight,  507.  Sights 
for  mobile  artillery,  509.  The  adjustable  or  tangent  sight,  509.  The 
panoramic  sight,  512.  The  range  quadrant,  514.  Telescopic  sights, 
517.  Telescopic  sight,  model  1904,  517.  Telescopic  sight,  model 
1898,  520.  The  power  and  field  of  view  of  telescopes,  522.  Aiming 
mortars,  522.  The  gunner's  quadrant,  523. 


XIV  CONTENTS. 

CHAPTER  XIV. 
Range  and  Position  Finding 525 

Range  finders,  525.  Depression  range  finders,  526.  Swasey  depres- 
sion range  and  position  finder,  526.  The  plotting  room,  527.  Field 
range  and  position  finding,  528.  The  Weldon  range  finder,  528.  The 
battery  commander's  telescope,  531.  The  battery  commander's 
ruler,  532.  Plotting  board  for  mobile  artillery,  537.  Other  range 
finders,  538.  The  Berdan  range  finder,  538.  The  Barr  and  Stroud 
range  finder,  538.  The  Le  Boulenge  telemeter,  540. 


CHAPTER  XV. 
Small  Arms  and  their  Ammunition 541 

Service  small  arms,  541.  The  38-caliber  revolver,  541.  The  Colt  auto- 
matic pistol,  544.  Modern  military  rifles,  546.  Requirements,  547. 
Life  of  the  rifle.  Erosion,  549.  The  U.  S.  magazine  rifle,  model  1903, 
550.  Appendages,  554.  Deviation.  Drift,  555.  The  22-caliber  gal- 
lery practice  rifle,  556. 

AMMUNITION  FOR  THE  SO-CALIBER  MAGAZINE  RIFLE,  556.  The  ball 
cartridge,  556.  Bullets,  559.  The  Blank  cartridge,  560.  The 
dummy  cartridge,  561.  The  guard  cartridge,  561.  Proof  of  ammu- 
nition, 562. 

CHAPTER  XVI. 
Machine  Guns 564 

Service  machine  guns,  564.  The  Gatling  machine  gun,  565.  The 
Maxim  automatic  machine  gun,  569.  The  Maxim  one-pounder  auto- 
matic gun,  574.  The  Colt  automatic  machine  gun,  575. 


CHAPTER  XVII. 
Submarine  Mines  and  Torpedoes.     Submarine  Torpedo  Boats .  .    576 

SUBMARINE  MINES  AND  TORPEDOES,  576.  History,  576.  Confederate 
mines,  578.  Spanish  mechanical  mine,  580.  Electric  mines,  581. 
Buoyant  mines,  581.  Ground  mines,  582.  The  explosive,  582.  The 
charge,  583.  Defensive  mine  systems,  583.  Countermining,  585. 
The  removal  of  mines,  585.  Mobile  and  automobile  torpedoes,  586. 
The  Sims-Edison  torpedo,  586.  The  Whitehead  torpedo,  586.  The 
Bliss-Leavitt  torpedo,  588.  The  Howell  torpedo,  589. 

SUBMARINE  TORPEDO  BOATS,  590.  The  Holland  submarine  torpedo 
boat,  591.  The  Lake  submarine  torpedo  boat,  592. 


TABLES. 

Table      I.  LOGARITHMS  OF  THE  X  FUNCTIONS 

Table    II.  HEATS  OF  FORMATION  OF  SUBSTANCES 

Table  III.  SPECIFIC  HEATS  OF  SUBSTANCES 

Table  IV.  DENSITIES  AND  MOLECULAR  VOLUMES  OF  SUBSTANCES 

Table    V.  ATOMIC  WEIGHTS 

Table  VI,  CONVERSION;    METRIC  AND  ENGLISH  UNITS,  TEMPERATURES. 


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ORDNANCE  AND  GUNNERY. 


CHAPTER  I. 
GUNPOWDERS. 

I.  Definitions. — Explosion,  in  a  general  sense,  may  be  defined 
as  a  sudden  and  violent  increase  in  the  volume  of  a  substance. 
In  a  chemical  sense,  explosion  is  the  extremely  rapid  conversion 
of  a  solid  or  a  liquid  to  the  gaseous  state,  or  the  instantaneous 
combination  of  two  or  more  gases  accompanied  by  increase  of 
volume.  Chemical  explosion  is  always  accompanied  by  great 
heat. 

An  explosion  due  to  physical  causes  alone,  as  when  a  gas 
under  compression  is  suddenly  released  and  allowed  to  expand, 
causes  cold. 

The  explosion  of  gunpowder  may  be  divided  into  three  parts: 
ignition,  inflammation,  and  combustion. 

Ignition  is  the  setting  on  fire  of  a  part  of  the  grain  or  charge. 

Gunpowder  is  ignited  by  heat,  which  may  be  produced  by 
electricity,  by  contact  with  an  ignited  body,  by  friction,  shock, 
or  by  chemical  reagents. 

An  ordinary  flame,  owing  to  its  slight  density,  will  not  ignite 
powder  readily.  The  time  necessary  for  ignition  will  vary  with 
the  condition  of  the  powder.  Thus  damp  powder  ignites  less 
easily  than  dry;  a  smooth  grain  less  easily  than  a  rough  one;  a 
dense  grain  less  easily  than  a  light  one. 


2  ORDNAXCE  AXD  GUNNERY. 

Powder  charges  in  guns  are  ignited  by  primers,  which  are  fired 
by  electricity,  by  friction,  or  by  percussion. 

Inflammation  is  the  spread  of  the  ignition  from  point  to  point 
of  the  grain,  or  from  grain  to  grain  of  the  charge. 

With  small  grain  powders  the  spaces  between  the  grains  are 
small,  and  the  time  of  inflammation  is  large  as  compared  with  the 
time  of  combustion  of  a  grain;  but  with  modern  large  grain  powders 
the  facilities  for  the  spread  of  ignition  and  the  time  of  burning  of 
the  grain  are  so  great  that  the  whole  charge  is  supposed  to  be 
inflamed  at  the  same  instant,  and  the  tune  of  inflammation  is  not 
considered. 

Combustion  is  the  burning  of  the  inflamed  grain  from  the  sur- 
face of  ignition  inward  or  outward  or  both,  according  to  the 
form  of  the  grain. 

Experiment  shows  that  powder  burns  in  the  air  according  to 
the  following  laws: 

1.  In  parallel  layers,  with  uniform  velocity,  the  velocity  being 
independent  of  the  cross  section  burning. 

2.  The  velocity  of  combustion  varies  inversely  with  the  density 
of  the  powder. 

When  a  charge  of  powder  is  ignited  in  a  gun  inflammation  of 
the  whole  charge  is  rapidly  completed.  The  gases  evolved  from 
the  burning  grains  accumulate  behind  the  projectile  until  the 
pressure  they  exert  is  sufficient  to  overcome  the  resistance  of  the 
projectile  to  motion.  The  accumulated  gases,  augmented  by 
those  formed  by  the  continued  burning  of  the  charge,  expand  into 
the  space  left  behind  the  projectile  as  it  moves  through  the  bore, 
exerting  a  continual  pressure  on  the  projectile  and  increasing  its 
velocity  until  it  leaves  the  muzzle. 

History. — The  Chinese  are  said  to  have  employed  an  explo- 
sive mixture,  very  similar  to  gunpowder,  in  rockets  and  other 
pyrotechny  as  early  as  the  seventh  century. 

The  earliest  record  of  the  use  in  actual  war  of  the  mixture  of 
charcoal,  niter,  and  sulphur  called  gunpowder,  dates  back  to  the 
fourteenth  century.  Its  use  in  war  became  general  at  the  begin- 


GUNPOWDERS.  3 

ning  of  the  sixteenth  century.  Until  the  end  of  the  sixteenth 
century  it  was  used  in  the  form  of  fine  powder  or  dust.  To  over- 
come the  difficulty  experienced  in  loading  small  arms  from  the 
muzzle  with  powder  in  this  form,  the  powder  was  at  the  end  of 
the  sixteenth  century  given  a  granular  form.  With  the  same 
end  in  view  attempts  at  breech  loading  were  made;  but  without 
success,  as  no  effective  gas  check,  which  would  prevent  the  escape 
of  the  powder  gases  to  the  rear,  was  devised. 

No  marked  improvement  was  made  in  gunpowder  until  1860, 
when  General  Rodman,  of  the  Ordnance  Department,  U.  S.  Army, 
discovered  the  principle  of  progressive  combustion  of  powder,  and 
that  the  rate  of  combustion,  and  consequently  the  pressure  exerted 
in  the  gun,  could  be  controlled  by  compressing  the  fine  grained 
powder  previously  used  into  larger  grains  of  greater  density. 
The  rate  or  velocity  of  combustion  was  found  to  diminish  as  the 
density  of  the  powder  increased.  The  increase  in  size  of  grain 
diminished  the  surface  inflamed,  and  the  increased  density 
diminished  the  rate  of  combustion,  so  that,  in  the  new  form, 
the  powder  evolved  less  gas  in  the  first  instants  of  combustion, 
and  the  evolution  of  gas  continued  as  the  projectile  moved  through 
the  bore.  By  these  means  higher  muzzle  velocities  were  attained 
with  lower  maximum  pressures.  To  obtain  a  progressively 
increasing  surface  of  combustion  General  Rodman  proposed  the 
perforated  grain,  and  the  prismatic  form  as  the  most  convenient 
for  building  into  charges.  As  a  result  of  his  investigations  powder 
was  thereafter  made  in  grains  of  size  suitable  to  the  gun  for  which 
intended,  small  grained  powder  for  guns  of  small  caliber,  and 
large  grained  powder  for  the  larger  guns.  The  powders  of  regu- 
lar granulation,  such  as  the  cubical,  hexagonal,  and  sphero-hex- 
agonal,  came  into  use,  and  finally  for  larger  guns  the  prismatic 
powder  in  the  form  of  perforated  hexagonal  prisms. 

A  further  control  of  the  velocity  of  combustion  of  powder 
was  obtained  in  1880  by  the  substitution  of  an  underburnt  char- 
coal for  the  black  charcoal  previously  used.  The  resulting  powder, 
called  brown  or  cocoa  powder  from  its  appearance,  burned  more 


ORDNANCE  AND  GUNNERY. 


slowly  than  tne  black  powder,  and  wholly  replaced  that  powder 
in  the  larger  guns. 

A  still  further  advance  in  the  improvement  of  powder  was 
brought  about  in  1886  by  the  introduction  of  smokeless  powders. 
These  powders  are  chemical  compounds,  and  not  mechanical  mix- 
tures like  the  charcoal  powders;  they  burn  more  slowly  than  the 


Sphero-hexagonal.  Prismatic. 

charcoal  powders,  and  produce  practically  no  smoke.  Smokeless 
powders  have  now  almost  wholly  replaced  black  and  brown  pow- 
ders for  charges  in  guns.  Black  powder  is  used  in  fuses,  primers, 
and  igniters,  in  saluting  charges,  and  as  hexagonal  powder  in 
the  smaller  charges  for  seacoast  mortars. 

2.  Charcoal  Powders. — COMPOSITION. — Black  gunpowder  is 
a  mechanical  mixture  of  niter,  charcoal,  and  sulphur,  in  the 
proportions  of  75  parts  niter,  15  charcoal,  and  10  sulphur. 

The  niter  furnishes  the  oxygen  to  burn  the  charcoal  and  sul- 
phur. The  charcoal  furnishes  the  carbon,  and  the  sulphur  gives 
density  to  the  grain  and  lowers  its  point  of  ignition. 

The  distinguishing  characteristic  of  charcoal  is  its  color,  being 
brown  when  prepared  at  a  temperature  up  to  280°,  from  this  to 
340°  red,  and  beyond  340°  black. 

Brown  powder  contains  a  larger  percentage  of  niter  than 
black  powder,  and  a  smaller  percentage  of  sulphur.  A  small 
.percentage  of  some  carbohydrate,  such  as  sugar,  is  also  added. 
Its  color  is  due  to  the  underburnt  charcoal. 


GUNPOWDERS.  5 

MANUFACTURE. — The  ingredients,  purified  and  finely  pulver- 
ized, are  intimately  mixed  in  a  wheel  mill  under  heavy  iron  rollers. 
The  mixture  is  next  subjected  to  high  pressure  in  a  hydraulic 
press.  The  cake  from  the  press  is  broken  up  into  grains  by  rollers, 
and  the  grains  are  rumbled  in  wooden  barrels  to  glaze  and  give 
uniform  density  to  their  surfaces.  The  powder  is  then  dried  in 
a  current  of  warm  dry  air,  and  the  dust  removed.  The  powder 
is  thoroughly  blended  to  overcome  as  far  as  possible  irregularities 
in  manufacture. 

For  powders  of  regular  granulation  the  mixture  from  the 
wheel  mill  was  broken  up  and  pressed  between  die  plates  con- 
structed to  give  the  desired  shape  to  the  grains.  Prismatic 
powder  was  made  by  reducing  the  mill  cake  to  powder  and  press- 
ing it  into  the  required  form. 

Smokeless  Powders. — There  are  two  classes  of  smokeless 
powders  used  in  our  service:  nitroglycerine  powder  in  small 
arms,  and  nitrocellulose  powder  in  cannon.  They  are  both  made 
from  guncotton,  to  which  is  added  for,  the  small-arm  powder 
about  30  per  cent  by  weight  of  nitroglycerine. 

COMPARISON  OF  NITROGLYCERINE  AND  NITROCELLULOSE  POW- 
DERS.— The  temperature  of  explosion  of  nitroglycerine  powder  is 
higher  than  that  of  nitrocellulose  powder.  As  the  erosion  of  the 
metal  of  the  bore  of  the  gun  is  found  to  increase  with  the  tem- 
perature of  the  gases,  greater  erosion  follows  the  use  of  nitro- 
glycerine powder.  The  endurance,  or  life,  of  a  modern  gun  is 
dependent  on  the  condition  of  the  bore,  and  on  account  of  the 
great  cost  of  cannon  erosion  becomes  a  more  serious  defect  in 
cannon  than  in  small  arms.  On  this  account,  therefore,  nitro- 
cellulose powder  is  more  suitable  than  nitroglycerine  powder  for 
cannon. 

To  produce  a  given  velocity  a  larger  charge  of  nitrocellulose 
than  of  nitroglycerine  powder  is  required.  This  necessitates  for 
nitrocellulose  powder  a  larger  chamber  in  the  gun,  and  the  increase 
in  size  of  the  chamber  involves  increased  weight  of  metal  in  the 
gun.  This  is  more  objectionable  in  a  small  arm  than  in  cannon, 


6  ORDNANCE  AND  GUNNERY. 

for  the  increased  weight  of  the  gun  and  of  the  charge  adds  to 
the  burden  of  the  soldier.  For  this  reason  nitroglycerine  powder 
is  more  suitable  than  nitrocellulose  powder  in  the  small  arm. 

In  the  manufacture  of  nitroglycerine  powders  for  cannon,  a 
satisfactory  degree  of  stability  under  all  the  conditions  to  which 
cannon  powders  are  exposed  was  not  obtained.  In  time  the 
powder  deteriorated,  and  exudation  of  free  nitroglycerine  oc- 
curred. Detonations  and  the  bursting  of  guns  followed.  In  the 
small-arm  cartridge  the  powder  is  hermetically  sealed,  and  as 
now  manufactured  appears  to  possess  a  satisfactory  degree  of 
stability. 

For  these  reasons  nitroglycerine  powder  has  been  selected  for 
use  in  small  arms  in  our  service,  and  nitrocellulose  powder  for 
use  in  cannon. 

A  disadvantage  attending  the  use  of  nitrocellulose  powder 
arises  from  the  fact  that  in  the  explosion  there  is  not  a  suffi- 
cient amount  of  oxygen  liberated  to  combine  with  the  carbon 
and  form  CO2.  The-  reaction  on  explosion  is  approximately 
represented  by  the  following  equation. 

2(C6H702)O3(NO2)3  =  9CO+3C02-f7H2O-f3N2 

A  large  quantity  of  CO,  an  inflammable  gas,  is  often  left  in  the 
bore.  On  opening  the  breech  more  oxygen  is  admitted  with 
the  air,  and  should  a  spark  be  present  the  CO  burns  violently, 
uniting  with  the  oxygen  and  forming  CO2.  This  burning  of  the 
gas  is  called  a  flareback.  An  instance  of  it  *has  occurred  with 
disastrous  results  in  a  turret  gun  aboard  one  of  our  men-of-war, 
the  Missouri. 

3.  Guncotton. — Guncotton  forms  the  base  of  most  smoke- 
less powders.  When  dry  cotton,  C6Hi0Oo,  is  immersed  in  a 
mixture  of  nitric  and  sulphuric  acids  part  of  the  hydrogen  of 
the  cotton  is  replaced  by  N02  from  the  nitric  acid.  The  sul- 
phuric acid  takes  up  the  water  formed  during  the  reaction  and 
prevents  the  dilution  of  the  nitric  acid.  The  nitrated  cotton, 


GUNPOWDERS.  7 

or  nitrocellulose,  may  be  of  several  orders  of  nitration,  depending 
on  the  strength  and  proportions  of  the  acids,  and  the  tempera- 
ture and  duration  of  immersion;  as  mononitrocellulose,  di- 
nitrocellulose,  trinitrocellulose,  according  as  one  or  more  atoms 
of  hydrogen  are  replaced.  All  nitrocellulose  is  explosive,  and 
the  order  of  explosion  produced  is  higher  as  the  nitration  is  higher. 
Dinitrocellulose  and  trinitrocellulose  are  used  in  the.  manu- 
facture of  smokeless  powders.  The  lower  orders  of  nitrocellulose, 
containing  less  than  12.75  per  cent  of  nitrogen,  are  soluble  in 
a  mixture  of  alcohol  and  ether.  Trinitrocellulose  contains  a 
higher  percentage  of  nitrogen,  and  is  insoluble  in  alcohol  and 
ether  but  soluble  in  acetone. 

MANUFACTURE  OF  GUNCOTTON  FOR  SMOKELESS  POWDERS.— 
The  process  followed  is  practically  the  same  for  all  varieties,  the 
nitration  being  stopped  at  the  point  desired  in  each  case. 

The  cotton  used  is  the  waste  or  clippings  from  cotton  mills. 
It  is  first  finely  divided  and  then  freed  from  grease,  dirt,  and  other 
impurities  by  boiling  with  caustic  soda.  After  cleansing  it  is 
passed  through  a  centrifugal  wringer  and  then  further  dried  in 
a  dry-house. 

The  dry  cotton  is  immersed  in  a  mixture  of  about  three  parts 
sulphuric  acid  and  two  parts  nitric  acid  for  about  fifteen  minutes; 
after  which  the  cotton  is  run  through  a  wringer  to  remove  as 
much  acid  as  possible.  It  is  then  thoroughly  washed  or  drowned. 

After  this  washing  the  guncotton  is  reduced  to  a  pulp  and 
further  washed  to  remove  any  trace  of  acid  which  may  have  been 
freed  in  pulping,  carbonate  of  soda  being  added  to  neutralize 
the  acid. 

The  water  is  then  partially  removed  from  the  pulp  by  hy- 
draulic pressure,  and  the  dehydration  is  completed  by  forcing 
alcohol  under  high  pressure  through  the  compressed  cake. 

4.  Nitroglycerine  Small-arm  Powder.— Laflin  and  Rand, 
W.  A. — In  the  manufacture  of  this  powder  highly  nitrated  gun- 
cotton  called  insoluble  nitrocellulose  is  used.  It  is  insoluble  in 
ether  and  alcohol  but  soluble  in  acetone. 


8  ORDNANCE  AND  GUNNERY. 

The  powder  is  composed  of 

Insoluble  nitrocellulose 67.25  per  cent 

Nitroglycerine 30.00  per  cent 

Metallic  salts 2.75  per  cent 

Forty  pounds  of  acetone  serve  as  solvent  for  100  pounds  of  the 
above  mixture. 

The  nitroglycerine  and  acetone  are  first  mixed.     The  acetone 

o  •/ 

makes  the  nitroglycerine  less  sensitive  to  pressure  or  shock,  and 
therefore  less  dangerous  to  handle  in  the  subsequent  operations. 
The  dried  guncotton  is  spread  in  a  large  copper  pan,  the  finely 
ground  metallic  salts  are  sifted  over  it,  and  the  mixed  nitrogly- 
cerine and  acetone  are  sprinkled  over  both;.  The  whole  is  mixed 
by  hand  by  means  of  a  wooden  rake  for  a  period  of  about  ten 
minutes,  the  object  of  the  mixing  being  to  thoroughly  moisten 
the  guncotton  for  the  purpose  of  eliminating  the  danger  from 
the  presence  of  dry  guncotton  in  the  next  operation.  The  mixed 
mass  is  put  into  a  mixing  machine,  where  it  is  mechanically  mixed 
for  a  period  of  three  hours.  It  comes  from  the  mixing  machine 
in  the  form  of  a  colloid  or  jelly  like  paste.  It  is  then  stuffed 
and  compressed  into  brass  cylinders,  from  which  it  is  forced  by 
hydraulic  pressure  through  dies  fitted  with  mandrels.  It  comes 
from  the  die  in  the  form  of  a  long  hollow  string  or  tube,  and  is 
received  on  a  belt  which  carries  it  over  steam  pipes  into  baskets. 
The  drying  which  it  receives  while  on  the  belt  strengthens  the 
tube,  and  after  remaining  half  an  hour  in  the  baskets  it  becomes 
sufficiently  tough  to  be  cut  into  grains.  This  is  done  in  a  machine 
provided  with  revolving  knives.  The  resulting  grains  are  bead- 
shaped  single  perforated  cylinders  and  have  a  length  of  about 
one  twentieth  of  an  inch.  The  powder  is  dried  for  two  or  three 
weeks  at  a  temperature  not  to  exceed  110°  F.  It  is  then  thor- 
oughly mixed  twice  in  the  blending  barrels  and  graphited  at  the 
same  time.  It  is  carefully  screened  to  remove  large  grains,  dust, 
and  foreign  matter,  and  is  .packed  in  muslin  bags  in  metallic 
barrels  holding  100  pounds. 


GUNPOWDERS.  9 

Cordite. — This  is  an  English  nitroglycerine  powder,  composed 
of  58  per  cent  of  nitroglycerine,  37  per  cent  of  guncotton,  and 
5  per  cent  of  vaseline.  The  vaseline  serves  to  render  the  powder 
water  proof  and  improves  its  keeping  qualities.  For  small  arms 
the  powder  is  made  in  the  form  of  slender  cylindrical  rods,  the 
length  of  the  chamber  of  cartridge.  For  cannon  it  is  in  thicker 
and  longer  rods,  in  tubular  form,  or  in  the  form  of  perforated 
cylinders.  For  heavy  guns  a  powder  called  Cordite  M.  D. 
has  lately  been  introduced.  The  composition  (30  parts  nitro- 
glycerine, 65  parts  guncotton,  5  parts  vaseline)  is  very  simi- 
lar to  that  of  our  small-arm  powder.  The  reduction  in  the  per- 
centage of  nitroglycerine  was  made  for  the  purpose  of  lowering 
the  temperature  of  explosion  and  reducing  the  erosion  in  the 
bore. 

Wetteren  Powder. — A  nitroglycerine  powder  manufactured  at 
the  Royal  Belgian  Factory  at  Wetteren.  The  solvent  used  is 
amyl  acetate. 

5.  Manufacture  of  Nitrocellulose  Powder. — The  guncotton 
used  contains  12.65  per  cent  of  nitrogen,  and  is  soluble  in  the 
ether-alcohol  mixture.  It  is  prepared  as  previously  described, 
the  dehydration  with  alcohol  being  so  conducted  that  when  com- 
pleted the  proper  proportion  of  alcohol  for  solution  remains  in 
the  cake.  The  guncotton  cake  is  broken  up  and  ground  until 
it  is  free  from  lumps,  and  is  then  placed  in  a  mixing  machine 
with  the  proper  amount  of  ether,  two  parts  of  ether  to  one  of 
alcohol.  During  the  mixing  the  temperature  is  kept  at  5°  C. 
to  prevent  loss  of  the  solvent. 

The  powder  comes  from  the  mixing  machine  as  a  colloid,  and 
the  remaining  processes  are  similar  to  those  described  for  nitro- 
glycerine powder. 

After  graining,  the  solvent  is  recovered  by  forcing  heated  air 
over  the  powder.  The  ether  and  alcohol  vapors  are  collected 
and  afterwards  condensed  for  further  use.  The  powder  is  dried 
for  a  period  varying  from  six  weeks  to  three  months,  depending 
on  the  size  of  the  grain.  The  drying  is  never  complete,  a  small 


10  ORDNANCE  AND  GUNNERY. 

percentage  of  the  solvent  always  remaining,  but  care  is  taken 
that  the  remaining  percentage  shall  be  uniform. 

In  the  manufacture  of  all  powders  uniformity  in  the  product 
can  only  be  obtained  by  the  strictest  uniformity  in  the  quantities 
and  quality  of  the  substances  used,  and  in  the  conduct  of  the 
various  processes. 

Cannon  powders  are,  as  a  rule,  not  graphited. 

Other  Smokeless  Powders. — The  length  of  time  required 
for  the  drying  of  nitrocellulose  powders  has  led  to  the  develop- 
ment of  other  powders  that  require  little  or  no  time  to  dry. 

Two  such  powders  have  been  tested.  One,  stabilite,  is  com- 
posed of  nitrocellulose  with  or  without  nitroglycerine  and  a  sol- 
vent that  is  itself  an  explosive  and  not  volatile.  The  other  is 
similar  to  the  present  nitrocellulose  powders  except  that  dinitro- 
cellulose  is  used  in  its  manufacture  instead  of  trinitrocellulose. 

To  make  up  for  the  insufficiency  of  oxygen  in  nitrocellulose, 
already  referred  to,  a  number  of  smokeless  powders  are  made 
by  a  combination  of  nitrocellulose  with  nitroglycerine  or  with 
the  nitrates  of  barium,  potassium,  and  sodium.  The  nitroglyc- 
erine or  the  metallic  nitrates  furnish  the  oxygen  which  is  deficient 
in  the  nitrocellulose. 

E.  G.  Powder. — This  powder  contains  both  soluble  and  insolu- 
ble nitrocellulose  and  the  nitrates  of  barium,  potassium,  and 
sodium.  It  is  yellow  in  color  and  of  fine  granulation.  It  is  an 
easily  ignited  quick  burning  powder  and  is  used  in  our  service  in 
blank  small-arm  cartridges. 

Schultze  Powder,  the  type  of  smokeless  sporting  powders,  is  of 
constitution  similar  to  that  of  E.  C.  powder. 

Troisdorf  Powder,  used  in  the  German  service,  and  B.  N,  Pow- 
der, in  the  French  service,  are  other  powders  similarly  constituted. 
All  these  powders  differ  principally  in  the  proportion  of  the  ingre- 
dients, and  also  in  the  organic  substance  used  as  a  cementing 
agent. 

Maxim  Powder  is  composed  of  nitrocellulose,  both  soluble  and 
insoluble,  nitroglycerine,  and  a  small  percentage  of  sodium  carbonate. 


GUNPOWDERS.  11 

Form  and  Size  of  Grain. — For  most  cannon  in  our  service 
the  powder  is  formed  into  a  cylindrical  grain  with  seven  longi- 
tudinal perforations,  one  central  and  the  other  six  equally  dis- 
tributed midway  between  the  center  of  the  grain  and  its  circum- 
ference. A  uniform  thickness  of  web  is  thus  obtained.  The 
powder  is  of  a  brown  color  and  has  somewhat  the  appearance 
of  horn.  The  length  and  diameter  of  the  grain  vary  in  powders 
for  different  guns,  the  size  of  grain  increasing  with  the  caliber 
of  the  gun.  For  the  3-inch  rifle  the  grain  has  a  length  of  about 
|  of  an  inch  and  a  diameter  of  -fo  of  an  inch.  For  the  12-inch 
rifle  the  length  is  1^  inches  and  the  diameter  |  of  an  inch.  For 
some  of  the  smaller  guns  the  grains  are  in  the  form  of  thin  flat 
squares. 

In  other  services  cannon  powders  are  made  into  grains  of 
various  shapes.  Cubes,  solid  and  tubular  rods  of  circular  cross 
section,  flat  strips,  and  rolled  sheets  are  among  the  forms  that 
have  been  used. 

6.  Proof  of  Powders. — All  powders  used  by  the  Army  are 
furnished  by  private  manufacturers.  The  materials  and  processes 
employed  in  the  manufacture  are  prescribed  by  the  Ordnance 
Department  in  rigid  specifications,  and  the  manufacture  in  all 
its  stages  is  under  the  inspection  of  the  Department.  The  proof 
of  the  powder  consists  of  tests  made  to  determine  its  ballistic 
qualities,  its  uniformity,  and  its  stability  under  various  condi- 
tions. Its  ballistic  qualities  and  uniformity  are  determined  from 
proof  firings  made  in  the  gun  for  which  the  powder  is  intended. 
The  required  velocity  must  be  obtained  without  exceeding  the 
maximum  pressure  specified.  The  mean  variation  in  velocity 
in  a  number  of  rounds  must  not  exceed,  in  the  small  arm  12  feet 
per  second,  in  cannon  1  per  cent  of  the  required  velocity. 

The  stability  of  the  powder  under  various  conditions  is  deter- 
mined by  heat  tests,  and  by  a  number  of  special  tests.  For  small- 
arms  powder  the  heat  test  consists  in  subjecting  the  powder, 
pulverized,  to  a  temperature  of  150°  to  154°  F.  for  20  minutes. 
It  must  not  in  that  time  emit  acid  vapors,  as  indicated  by  the 


12  ORDNANCE   AND  GUNNERY. 

slightest  discoloration  of  a  piece  of  iodide  of  potassium  starch 
paper  partially  moistened  with  dilute  glycerine.  The  other  tests 
consist  in  exposing  the  powder  both  loose  and  loaded  in  car- 
tridges, to  heat,  cold,  and  moisture,  for  periods  varying  from  six 
hours  to  one  week.  When  fired  the  variations  in  velocities  and 
pressures  must  not  exceed  specified  limits. 

Nitrocellulose  cannon  powders  are  subjected  to  a  heat  of 
135°  C.  (275°  F.)  for  five  hours.  Acid  fumes,  as  indicated  by 
the  reddening  of  blue  litmus  paper,  must  not  appear  under  expo- 
sure of  an  hour  and  a  quarter,  nor  red  nitrous  fumes  under  two 
hours.  Explosion  must  not  occur  under  five  hours.  Other  tests 
are  made  for  the  determination  of  the  loss  of  weight  when  sub- 
jected to  heat,  of  the  moisture  and  volatile  matter  in  the  powder, 
of  the  quantities  of  nitrogen  in  the  powder,  and  of  ash  in  the 
cellulose. 

For  the  proper  regulation  of  the  evolution  of  gas  in  the  gun 
it  is  important  that  the  grains  of  smokeless  powder  retain  their 
general  shape  while  burning.  If  they  break  into  pieces  under  the 
pressure  to  which  they  are  subjected,  the  inflamed  surface  is 
increased,  gas  is  more  quickly  evolved,  and  the  pressure  in  the 
gun  is  raised.  The  powder  is  therefore  subjected  to  a  physical 
test  to  determine  that  the  grain  has  sufficient  strength  and  tough- 
ness. The  grains  are  cut  so  that  the  length  equals  the  diameter, 
and  are  then  subjected  to  slow  pressure  in  a  press.  The  grain 
must  shorten  35  per  cent  of  its  length  before  cracking. 

Powder  grains  incompletely  burned,  that  have  been  recovered 
after  firing,  show  that  the  burning  proceeds  accurately  in  parallel 
layers.  The  outer  diameter  of  the  grain  is  reduced  and  the  diam- 
eter of  the  perforations  increased  in  exactly  equal  amounts. 

7.  Advantages  of  Smokeless  Powder. — The  advantages  ob- 
tained by  the  use  of  smokeless  powder  are  due  almost  wholly 
to  the  fact  that  the  powder  is  practically  completely  converted 
into  gas.  The  experiments  of  Noble  and  Abel  show  that  the 
gases  evolved  by  charcoal  powders  amount  to  only  43  per  cent 
of  the  weight  of  the  powder,  and  part  of  the  energy  of  this  quan- 


GUNPOWDERS.  13 

tity  of  gas  is  expended  in  expelling  the  residue  from  the  bore.  A 
smaller  quantity  of  smokeless  powder  will  therefore  produce  an 
equal  weight  of  gas,  and  with  smaller  charges  we  may  give  to 
the  projectile  equal  or  higher  velocities.  The  smokelessness  of 
the  powder  and  the  absence  of  fouling  in  the  bore  are  also  due 
to  the  complete  conversion  of  the  powder  into  gas. 

Ignition  and  Inflammation  of  Smokeless  Powder. — Though 
the  temperature  at  which  smokeless  powder  ignites,  about  180° 
C.,  is  much  lower  than  that  required  for  the  ignition  of  black 
powder,  300°  C.,  the  complete  inflammation  of  a  charge  com- 
posed only  of.  smokeless  powder  takes  place  more  slowly  than 
the  inflammation  of  a  charge  of  black  powder.  This  is  due  to 
the  slower  burning  of  the  smokeless  powder  and  the  consequent 
delay  in  the  evolution  of  a  sufficient  quantity  of  the  heated  gas 
to  completely  envelop  the  grains  composing  the  charge.  In  the 
long  chamber  of  a  gun  the  gases  first  evolved  at  the  rear  of  the 
charge  may,  in  expanding,  acquire  a  considerable  velocity.  The 
pressure  due  to  their  energy  is  added  to  the  static  pressure  due 
to  their  temperature  and  volume,  thus  increasing  the  total  pres- 
sure in  the  gun.  The  movement  of  the  gases  back  and  forth 
causes  what  are  called  wave  pressures,  and  if  the  complete  ignition 
of  the  charge  is  delayed  until  the  projectile  has  moved  some 
distance  down  the  bore,  there  may  result  at  some  point  in  the 
gun  a  higher  pressure  than  the  metal  of  the  gun  at  that  point 
can  resist. 

For  this  reason  and  in  order  to  insure  the  practically  instan- 
taneous ignition  of  the  whole  charge,  small  charges  of  black  powder 
are  added  to  every  smokeless  powder  charge.  The  priming 
charges  of  black  powder  insure  against  hang-fires  and  misfires, 
and  by  producing  uniformity  of  inflammation  assist  toward  uni- 
formity in  the  ballistic  results. 

In  addition,  in  order  to  prevent  as  far  as  possible  the  pro- 
duction of  wave  pressures,  the  charge  of  powder,  whatever  its 
weight,  is  given  when  practicable  a  length  equal  to  the  length 
of  the  chamber. 


14  ORDNANCE  AND  GUNNERY. 

8.  Powder  Charges. — The  powder  for  a  charge  in  the  gun  is 
inserted  in  one  or  more  bags,  depending  upon  the  weight  of  the 
charge.  The  bags  are  made  of  special  raw  silk  and  are  sewed 
with  silk  thread.  The  ends  of  each  bag  are  double,  and  between 
the  two  pieces  at  each  end  is  placed  a  priming  charge  of  black 
powder,  quilted  in  in  squares  of  about  two  inches  and  uniformly 
spread  over  the  surface. 

The  charge  is  inserted  through  an  unsewed  seam  at  one  end, 
and  the  seam  is  then  sewed.  The  bag,  purposely  made  large, 
is  then  drawn  tight  around  the  charge  by  lacing  drawn  with  a 
needle  between  two  pleats  on  the  exterior.  Two  priming  pro- 
tector caps  are  then  drawn  over  the  ends  of  the  bag  and  fastened 
by  draw  strings.  In  the  bottom  of  each  cap  is  a  disk  of  felt  which 
serves  to  keep  moisture  from  the  priming  charge -and  prevents 
the  loss  of  the  priming  through  wearing  of  the  bottom  of  the 
bag.  For  convenience  in  handling  the  charge  a  cloth  strap  is 
attached  to  each  protector  cap.  By  means  of  the  straps  the  pro- 
tector caps  may  be  pulled  off  without  undoing  the  draw  strings 
when  the  charge  is  to  be  inserted  in  the  gun. 

The  illustrations  show  a  bag  filled  ready  for  lacing,  and  a 
bag  filled  and  laced  and  provided  with  the  priming  protector 
caps. 

The  weight  of  each  portion  of  the  charge  should  not  be 
greater  than  can  be  readily  carried  by  one  man.  Thus  the  charge 
of  360  pounds  for  the  12-inch  rifle  is  put  up  in  four  bags  each  hold- 
ing 90  pounds. 

As  previously  stated,  the  charge  whatever  its  weight  is  made 
up  if  practicable  of  a  length  nearly  equal  to  that  of  the  cham- 
ber, with  a  minimum  limit  of  nine  tenths  of  that  length. 

Raw  silk  does  not  readily  hold  fire.  With  powder  bags  made 
of  cotton  cloth  it  occasionally  happens  that  a  fragment  of  the 
bag  remains  burning  in  the  bore,  and  to  this  fact  is  ascribed  the 
flarebacks  that  have  occurred.  Powder  bags  treated  with  chem- 
icals to  render  them  non-inflammable  have  also  been  tried.  Am- 
monium phosphate  is  found  to  be  the  best  agent  for  this  purpose. 


Bag  filled  ready 
for  lacing 


Bag  laced  and  provided 
with  priming  pro- 
tector caps. 


SECTION  OF  POWDER  CHARGE  FOR  HEAVY  GUNS. 


16  ORDNANCE  AND  GUNNERY. 

COMBUSTION    OF    POWDER    UNDER   CONSTANT 
PRESSURE. 

9.  Quantity  Burned  when  any  Thickness  has  Burned.— 

Under  constant  pressure,  as  in  the  air,  a  grain  of  powder  burns 
in  parallel  layers  and  with  uniform  velocity,  in  directions  per- 
pendicular to  all  the  ignited  surfaces. 

Under  the  variable  pressure  in  the  gun  powder  burns  with 
a  variable  velocity,  but,  as  has  been  previously  stated,  modern 
smokeless  powders  burn  accurately  in  parallel  layers  in  the  gun. 
A  determination  of  the  volume  burned  when  any  thickness  of 
layer  is  burned  will  therefore  be  useful  when  we  come  to  con- 
sider the  burning  of  the  powder  in  the  gun. 

Powders   of  irregular  granulation  may  be  considered  as  com- 
posed of  practically  equivalent  grains  of  regular  form. 
Let  IQ  be  one  half  the  least  dimension  of  the  grain, 
I  the  thickness  of  layer  burned  at  the  time  t, 
So  the  initial  surface  of  combustion, 
S  the  surface  of  combustion  at  the  time  t,  when  a  thick- 
ness I  has  been  burned, 
Sf  the  surface  of  combustion  when  l  =  lo, 
VQ  the  initial  volume  of  the  grain, 
V  the  volume  burned  at  the  time  t, 
F  =  V/Vo  the  fraction  of  grain  burned  at  the  time  t. 
The  least  dimension  of  the  grain,  2Z0,  is  called  the  web  of  the 
grain.     As   the  burning  proceeds  equally   in  directions  perpen- 
dicular to  all  the  surfaces,  the  grain  will,  in  most  instances,  be 
about  to  disappear  when  the  thickness  of  layer  burned  is  nearly 
equal  to  ZQ.    The  surface  Sf,  corresponding  to   this   thickness,  is 
therefore  called  the  vanishing  surface. 

A  general  expression  may  be  written  for  the  burning  surface 
of  a  grain  when  a  thickness  I  has  been  burned.  Since  a  surface 
is  a  quantity  of  the  second  degree  the  expression  will  be  of  the 
form, 

(1) 


GUNPOWDERS.  17 

in  which  a  and  6  are  numerical  coefficients  whose  values  depend 
on  the  form  and  dimensions  of  the  grain-. 

For  grains  that  burn  with  a  decreasing  surface  the  sign  of 
a  in  this  equation  will  later  be  found  to  be  negative,  and  for  those 
that  burn  with  an  increasing  surface  the  sign  of  b  becomes  nega- 
tive. 

The  volume  burned  when  any  thickness  I  has  been  burned  is 


=  flSdl 
Jo 


And  substituting  for  S  its  value  from  equation  (1), 

P  (2) 


Dividing  both  members  by  V0  and  introducing  10  by  multiplica- 
tion and  division  we  have,  for  the  fraction  of  the  grain  burned, 


o23_S0l0  I  f       oZo|    Wj 

Fo  =  V0  lo(    +2S010+3S0102 

and  making 

a=S0lo/V0        l=alo/2S0        fjL  =  bl02/3S0  (3) 

we  obtain 


This  equation  gives  the  value  for  the  fraction  of  the  grain 
burned  when  a  length  I  has  been  burned;  and  as  each  grain  in 
a  charge  of  powder  burns  in  the  same  manner,  the  equation  also 
expresses  the  value  for  the  fraction  of  the  whole  charge  burned. 

The  quantities  a,  X,  and  //  are  called  the  constants  of  form 
of  the  powder  grain.  Their  values  depend  wholly  on  the  form 
and  relative  dimensions  of  the  grain. 


18  ORDNANCE  AND  GUNNERY. 

When  1  =  10  the  whole  grain  is  burned,  F  becomes  unity,  and 
we  have  the  relation  • 

l=a(l  +  J+jtt)  (5) 

which  may  always  serve  to  test  the  correctness  of  the  values 
of  these  constants  as  determined  for  any  grain. 

10.  Determination  of  the  Values  of  the  Constants  of  Form 
for  Different  Grains.  —  In  the  values  of  a,  X,  and  //,  equations  (3), 
the  quantities  So,  lo,  and  V0  are  known  for  any  form  of  grain. 
We  must  know  in  addition  the  values  of  a  and  6. 

When  1  =  10  the  volume  burned  is  the  original  volume  Vo 
and  equation  (2)  becomes 


The  burning  surface  at  this  time,  designated  by  S',  is,  from 
equation  (1), 


The  values  of  a  and  6,  if  desired,  may  be  derived  from  these 
two  equations. 

Combining  the  two  equations  with  equations  (3)  we  obtain 
the  following  values  for  a,  ^,  and  /*. 


=  3/a-S'/S0-2 


(6) 


The  Vanishing  Surface. — The  quantity  Sf,  which  represents 
the  vanishing  surface,  or  surface  of  combustion  when  1  =  10,  re- 
quires explanation.  A  spherical  grain  burning  equally  along  all 
the  radii  becomes  a  point  as  I  becomes  equal  to  10.  S'  for  a 
sphere  is  therefore  0,  and  similarly  for  a  cube.  A  cylindrical 
grain,  of  length  greater  than  its  diameter,  becomes  a  line  when 
l  =  lo.  S'  is  therefore  0  for  this  cylinder.  A  flat  square  grain 


GUNPOWDERS.  19 

remains  flat  throughout  the  burning,  its  thickness  being  reduced 
until  as  I  becomes  equal  to  10  there  are  two  burning  surfaces  with 
no  powder  between  them.  S',  in  this  case,  is  the  sum  of  these 
two  surfaces. 

PARALLELOPIPEDON.  —  Let  2Z0  be  the  least  dimension,  and  m 
and  n  the  other  dimensions  of  the  grain  of  powder,  m  being  the 
longer. 

So  =  4Z0m  -1-  4Z0n  +  2mn 
S'=2(m-2lo)(n-2l0) 


Make  x  and  y  the  ratios  of  the  least  dimension  to  the  other  dimen- 
sions of  the  grain 

x  =  2l0/m  y  =  2l0/n 

With  these  values  we  get  from  (3)  for  a 


Eliminating  the  common  factors  in  the  values  of  S'  and  So 
we  have, 

S'     mn-2l0n 


So         2lom+2l0n+mn 
and  dividing  each  term  by  mn, 

S'     l-2l0/m-2lo/n+4l02/mn     l-x-y+xy 
S0~          2lo/n+2lo/m+l  l+x+y 

Substituting  in  equations  (6), 

^_     x+y+xy 
l+x+y 

xy 


20  ORDNANCE  AND  GUNNERY. 

For  the  parallelopipedon  grain,  the  general  expression  for  the 
fraction  of  the  grain  burned  when  a  thickness  I  has  been  burned 
therefore  becomes,  by  equation  (4), 


And  by  giving  various  values  to  x  and  y  this  equation  may  be 
applied  to  any  form  of  the  parallelepiped. 

ii.  Cube.  —  For  instance,  for  the  cube  m  =  n  =  2l0,  and  x  and  y 
are  unity.    Therefore 


and 

L[    1    IJ! 

71 T"    "*"   ~"Z  J~2 

tQ  L  M)  "  ^0 

££np. — For  strips  or  ribbons  of  square  cross  section  n  =  2Zo 
and  y  =  l, 

_  l  +  2x  x 

CX.       *j  ~(   *C  A  ^    ~ 

2  +  x  2  +  x 

If  the  strip  is  very  long  in  comparison  with  the  edge  of  cross 
section,  x  is  practically  zero  and 

Square  Flat  Grains. — For  square  flat  grains  x  =  y  and 


A—— 


,  ,  0  -  ,  0 

1  +  2x  l  +  2x 

If  the  grains  are  very  thin,  x  is  small  compared  with  unity  and 


As  the  surface  and  volume  of  a  burning  sphere  of  powder  vary 
with  the  diameter  in  precisely  the  same  manner  that  the  surface 


GUNPOWDERS.  21 

and  volume  of  a  cube  vary  with  the  edge  of  the  cube,  the  values 
a,  A,  and  /*,  see  equations  (6),  will  be  the  same  for  the  sphere 
as  for  the  cube.  And  similarly  the  values  of  these  constants  for 
a  cylinder  of  length  greater  than  its  diameter  will  be  the  same  as 
forHhe  strips  of  square  cross  section,  and  the  values  for  a  flat 
cylinder  will  be  the  same  as  for  the  flat  square  grain. 
SPHERE.;  —  For  the  sphere, 


the  same  as  for  the  cube. 

12.  SOLID  CYLINDER.  —  For  the  solid  cylinder  of  length  greater 
than  the  diameter,  d  =  2l0  and  x  =  2l0/m, 


2+x 

If  the  diameter  is  very  small  compared  with  the  length,  as  in 
the  slender  cylinders  or  threads  of  cordite,  210  is  small  with  respect 
to  m,  x  is  small  compared  with  unity,  and  approximately 

a  =2  A  =-1/2  /£=0 

Therefore  for  cordite 


FLAT  CYLINDER.  —  210  =  thickness,  d  =  diameter,  x  =  2l0/d, 


the  same  as  for  the  flat  square  grain. 

SINGLE  PERFORATED  CYLINDER.  —  Let  R  be  the  outer  radius  of 
the  grain,  r  the  radius,  of  the  perforation,  and  m  the  length  of  the 


22 


ORDNANCE  AND  GUNNERY. 


grain.     Make  x  =  2lo/m.    By  proper  substitution  we  find,  for  the 
tubular  grain  in  general, 


If  the  grain  is  very  long  compared  with  its  thickness  of  wall, 
x  is  small  compared  with  unity.     We  then  have 


and 


/i=0 


(10) 


This  indicates  for  long  tubes  with  thin  walls  a  constant  emis- 
sion of  gas  during  the  burning  of  the  grain,  since  F  now  varies 
directly  with  I. 

13.  MULTIPERFORATED  CYLINDER.  —  A  section  of  the  service 
multiperf  orated  grain  before  burning  is  shown  in  Fig.  1.  The 


FIG.  1. 


FIG.  2. 


perforations  are  equal  in  diameter  and  symmetrically  distributed. 
The  web,  2lo,  is  the  thickness  between  any  two  adjacent  circum- 
ferences. When  this  thickness  has  burned  the  section  is  as  shown 
in  Fig.  2. 

There  remain  now  six  interior  and  six  exterior  three-cornered 
pieces,  called  slivers,  which  burn  with  a  decreasing  surface  until 
completely  consumed. 

The  method  previously  followed  cannot  be  used  to  find  the 
value  of  F  for  the  multiperf  orated  grain  because  the  law  of  burn- 


GUNPOWDERS. 


23 


ing  for  this  grain  changes  abruptly  when  the  grain  is  but  partially 
consumed. 

To  find  the  value  of  F  for  this  grain  we  proceed  as  follows. 

Let  R  be  the  radius  of  the  grain,  r  the  radius  of  each  perfora- 
tion, m  the  length  of  the  grain. 

For  the  initial  volume  we  have 


When  a  thickness  I  is  burned,  R,  r,  and  m  become  respectively 
R—  I,  r+l,  and  m—2l,  and  the  volume  remaining  is  obtained  from 
the  above  equation  by  making  these  substitutions.  The  differ- 
ence between  the  two  volumes  will  be  the  volume  burned,  and 
dividing  this  resulting  volume  by  VQ  we  have  the  value  of  F. 
This  may  be  reduced  to 


2lo\R2-7r2+m(R+7r')} 

•»    ~~  -_./TV>       *r__o\  ~"    7    1  •••    i 


F) 

tfl      J 


R2-7r2  + 
For  the  service  multiperf orated  grain  we  therefore  have 


(ID 


ct  = 


m(R2-7r2) 


(12) 


Equation  (11)  applies  only  while  the  web  of  the  grain  is  burn- 
ing and  does  not  apply  to  the  slivers. 

The  thickness  of  web  bears  the  following  relation  to  R  and  r 


24  ORDNANCE  AND  GUNNERY. 

in  our  service  grains,  as  may  be  readily  seen  by  drawing  a  diam- 
eter through  any  three  perforations,  Fig.  1. 

D-3d_R-3r 
Mo-  —-         —  —  (Id) 


We  will  take  a  specific  grain  for  use  later  to  illustrate  the 
burning  of  the  multiperf  orated  cylinder.  The  grains  of  a  lot  of 
powder  for  the  8-inch  rifle  had  the  following  dimensions,  in  inches. 

fl  =  0.256  r  =  0.0255  m  =  1.029 

Therefore,  from  (13),  10  =  0.044875. 

Substituting  in  (11),  we  obtain  for  this  grain 

F  =  0.72667r  1  1  +  0.19590^--  0.02378^-  1  (14) 

tO  I  HJ  i(f  } 

When  I  =  lo,  that  is,  when  the  grain  is  reduced  to  slivers, 

F  =  0.85174 

from  which  we  see  that  the  slivers  form  about  15  per  cent  of  this 
particular  grain. 

14.  Emission  of  Gas  by  Grains  of  Different    Forms.—  As 

the  velocity  of  combustion  under  constant  pressure  is  uniform, 
the  time  of  burning  will  be  proportional  to  the  thickness  of  layer 
burned. 

We  may  conveniently  show  the  manner  of  burning  of  the 
different  grains  by  dividing  the  half  web  into  five  layers  of  equal 
thickness,  that  is,  by  giving  to  the  ratio  1/10,  in  the  value  of  the 
fraction  burned,  the  values  1/5,  2/5,  etc.,  in  succession,  and 
then  tabulating  the  resulting  values  of  F.  The  successive  values 
of  F  obtained  will  be  the  fractional  parts  burned  in  1/5,  2/5, 
etc;,  of  the  total  time  of  burning;  and  the  differences  of  the  suc- 
cessive values  of  F  will  be  the  fractions  burned  in  the  successive 
intervals  of  time. 


GUNPOWDERS. 


25 


The  following  table  is  formed  from  equations  (8),  (9),  and 
(14).  For  the  multiperf orated  grain  the  fractions  1/1Q  are  frac- 
tions of  the  web  only. 


l/lo 

Cube. 

Slender  Cylinder. 

Multiperforated  Cylinder. 

F. 

Difference. 

F. 

Difference. 

F. 

Difference. 

0.0 

0.000 

0.00 

0.00 

0.49 

0.36 

0.15 

0.2 

0.49 

0.36 

0.15 

0.29 

.0.28 

0.16 

0.4 

0.78 

0.64 

0.31 

0.16 

0.20 

0.17 

0.6 

0.94 

0.84 

0.48 

0.05 

0.12 

0.18 

0.8 

0.99 

0.96 

0.66 

0.01 

0.04 

0.19 

1.0 

1.00 

1.00 

1.00 

1.00 

Web  0.85 

0.85 

0.15 

Whole  grain      1.00 

1.00 

Regarding  the  columns  of  differences  in  the  table  we  see 
that  nearly  half  of  the  cubical  grain  is  burned  in  the  first  layer, 
and  that  the  volume  burned  in  the  successive  layers  decreases 
continuously.  The  slender  cylinder  emits  at  first  a  less  volume 
of  gas  than  the  cube  and  later  a  greater  volume,  that  is,  its  burn- 
ing is  more  progressive.  We  have  seen,  equation  (10),  that  the 
long  tubular  grain  burns  with  a  constant  surface.  The  quantity 
of  gas  given  off  in  the  burning  of  each  layer  is  therefore  the  same, 
and  the  grain  is  more  progressive  than  the  slender  cylinder.  The 
multiperforated  cylinder  burns  with  a  continually  increasing 
surface  until  the  web  is  consumed,  and  the  volume  of  gas  given 
off  increases  for  each  layer  burned. 

Whether  the  burning  surface  of  the  multiperforated  grain 
increases  or  decreases  depends  on  the  relation  between  the  length 
of  the  grain  and  the  radii  of  the  grain  and  of  the  perforations. 
Referring  to  equation  (11)  it  will  be  seen  that  when 

(15) 


26  ORDNANCE  AND  GUNNERY. 

the  second  term  within  the  brackets  disappears,  m  is  the  length 
of  the  grain.  Giving  to  the  multiperforated  grain  considered  in 
equation  (14)  the  length  indicated  in  the  last  equation,  we  get 
w  =  0.29,  and  the  value  of  F  becomes 

F  =  0.94892^- !  1  -  0.08134^  1 
to  I  to2  J 

A  table  formed  from  this  equation  will  show  that  this  grain 
burns  with  a  continuously  decreasing  surface;  the  fractional 
volumes  burned  in  the  successive  intervals  being  0.189,  0.186, 
0.178,  0.167,  and  0.152.  The  sum  of  these,  0.872,  is  the  frac- 
tion of  the  grain  burned  when  the  web  ceases  to  burn. 

It  is  apparent  that  since  the  manner  of  burning  of  a  multi- 
perforated  grain  depends  upon  the  relation  expressed  in  equa- 
tion (15),  a  grain  may  start  to  burn  with  an  increasing  surface, 
and  change,  as  the  length  is  diminished,  to  burn  with  a  decreas- 
ing surface. 

The  multiperforated  grains  used  in  our  service  are  of  lengths 
considerably  greater  than  that  indicated  in  equation  (15).  The 
length  of  the  grain  is  about  2|  times  the  outer  diameter.  The 
diameter  of  the  perforations  is  about  1/10  the  exterior  diameter 
of  the  grain.  The  grains  burn  with  a  continuously  increasing 
surface  until  the  web  is  burned,  and  then  with  a  decreasing  sur- 
face. 

The  Weight  of  Charge  Burned. — Assuming  instant  ignition 
of  the  whole  charge,  equation  (4)  expresses  the  value  of  the  frac- 
tion of  the  charge  burned  when  any  thickness,  I,  has  burned. 

Let  CD  be  the  weight  of  the  charge, 

y  the  weight  burned  at  any  instant. 

The  fraction  of  the  charge  burned  is  therefore  y/a,  which 
we  may  write  for  F  in  equation  (4),  and  obtain 

I  (          I         I2 


I  GUNPOWDERS.  27 

15.  Consideration  as  to  Best  Form  of  Grain. —  It  would 
appear  that  the  most  desirable  form  of  powder  grain  would  be 
one  that  gives  off  gas  slowly  at  first,  starting  the  projectile  before 
a  high  pressure  is  reached,  and  then  with  an  increased  burning 
surface  and  a  more  rapid  evolution  of  gas  maintaining  the  pres- 
sure behind  the  projectile  as  it  moves  down  the  bore. 

It  is  this  consideration  .that  has  led  to  the  adoption  in  our 
service  of  the  multiperforated  grain,  which  in  the  preceding 
discussion  is  shown  to  be  the  only  practicable  form  of  grain  that 
burns  with  an  increasing  surface  emitting  successively  increasing 
volumes  of  gas.  The  facilities  for  complete  inflammation  of  the 
charge  are  not  as  great  in  this  grain  as  in  some  others,  as  the 
grains  assume  all  positions  in  the  cartridge  bag,  and  do  not  pre- 
sent unobstructed  channels  to  the  flame  from  the  igniter.  We 
have  seen,  page  13,  that  when  there  is  delay  in  the  complete 
inflammation  of  the  charge,  excessive  pressures,  called  wave  pres- 
sures, may  arise,  due  to  the  velocity  acquired  by  the  gases  first 
formed. 

The  single  perforated  cylinder,  or  tubular  grain,  offers  advan- 
tages in  this  respect.  This  grain  when  its  length  is  great  com- 
pared to  the  thickness  of  web,  as  when  cut  in  lengths  to  fit  the 
chamber,  burns  with  a  practically  constant  surface,  as  we  have 
seen,  equation  (10).  The  charge  is  readily  prepared  by  bind- 
ing the  grains  in  bundles,  and  when  so  prepared  offers  perfect 
facilities  for  the  prompt  spread  of  ignition  through  the  uniformly 
distributed  longitudinal  air  spaces  within  and  between  the  grains. 

While  larger  charges  of  powder  in  this  form  may  be  required, 
to  produce  a  desired  velocity,  the  advantages  of  greater  uni- 
formity in  velocities  and  pressures,  and  decreased  likelihood  of 
excessive  pressures,  will  probably  be  obtained  by  its  use. 

In  the  process  of  drying  the  tubular  grain  in  manufacture 
the  grain  will  warp  excessively  if  too  long  with  reference  to  its 
diameters.  On  this  account  and  in  order  that  the  grain  may 
serve  for  convenient  building  into  charges  its  length  is  limited. 
The  requirement  of  prompt  ignition  throughout  the  length  of  the 


28  ORDNANCE  AND  GUNNERY. 

grain  also  limits  its  length.    Good  results  have  been  obtained  with 
grains  whose  length  was  85  times  the  outer  diameter. 


VARIOUS    DETERMINATIONS. 

1  6.  To  Determine  the  Number  of  Grains  in  a  Pound.  —  Let 

n  be  the  number  of  grains  in  a  pound  of  powder, 
y0  the  volume  of  each  grain  in  cubic  inches, 
d  the  density  of  the  powder. 

The  volume  occupied  by  the  solid  powder  in  one  pound  is 
evidently  nV0;  the  volume  of  one  pound  of  water  is  27.68  cu. 
in.;  and  the  volumes  being  inversely  proportional  to  the  den- 

sities, we  obtain 

c       iT-k*^ 

27.68 


and  when  the  number  of  grains  in  a  pound  is  known,  we  have 
for  the  density 

(18) 


"  nV0 

To  Determine  the  Dimensions  of  Irregular  Grains.  —  Irreg- 
ular grains  may  be  considered  as  spheres,  and  the  mean  radius 
may  be  determined  as  follows.  Retaining  the  above  significa- 
tions of  n  and  VQ,  let  r  be  the  mean  radius  of  the  grains  in  inches. 

Then  y0  =  4^r3/3.  Substituting  this  in  the  above  equation 
and  solving  for  r  we  obtain 

1.8766 


Comparison  of  Surfaces. — Let  Si  be  the  total  initial  surface 
of  the  grains  in  a  pound  of  powder.  As  SQ  is  the  initial  surface 
of  each  grain, 


GUNPOWDERS. 


29 


Substituting  the  value  of  n  from  (17)  and  the  value  of  So  from 
the  first  of  equations  (3)  we  obtain 


_      27.68a 

01  = M 


(19) 


-c 


From  which  it  appears  that  for  two  charges  of  equal  weight, 
made  up  of  grains  of  the  same  density  and  thickness  of  web, 
the  initial  surfaces  of  the  two  charges  are  to  each  other  as  the 
values  of  a  for  the  two  forms  of  grain.  For  charges  of  equal 
weights  composed  of  grains  of  the  same  shape  and  density  the 
initial  surfaces  will  be  inversely  proportional  to  the  least  dimen- 
sions of  the  grains. 

17.  Density  of  Gunpowder. — The  density,  or  specific  gravity, 
of  gunpowder  is  the  ratio  of  the  weight  of  a  given  volume  of  solid 
powder  to  the  weight  of  an  equal 
volume  of  water.  The  density  of 
charcoal  gunpowders  is  determined 
by  means  of  an  instrument  called 
the  mercury  densimeter,  in  which  is 
obtained  the  weight  of  a  volume  of 
mercury  equal  to  the  volume  of  the 
powder.  From  the  known  specific 
gravity  of  the  mercury  that  of  the 
powder  is  readily  determined.  Mer- 
cury is  used  in  the  instrument  instead 
of  water  because  mercury  possesses 
the  property  of  closely  enveloping 
the  grains  of  powder  without  being 
absorbed  into  their  pores,  and  it 
does  not  dissolve  the  constituents  of 
the  powder. 

The  densimeter  is  shown  in  the 
accompanying  figure.    The  glass  globe 
a  is  connected  with  an  air  pump  by 
the  rubber  tube  c.    The  lower  outlet  of  the  globe  is  immersed 
in  mercury  in  the  dish  d. 


FIG.  3. 


30  ORDNANCE  AND  GUNNERY. 

As  the  globe  is  exhausted  of  air  by  means  of  the  air  pump,  the 
mercury  is  drawn  upward  until  it  fills  the  globe  and  stands  at  a 
certain  height  in  the  glass  tube  e.  The  globe  is  then  detached, 
full  of  mercury,  and  weighed.  It  is  then  emptied,  and  a  given 
weight  of  powder  placed  in  it.  The  globe  is  then  returned  to  its 
original  position,  the  air  again  exhausted,  and  mercury  allowed  to 
enter  until  it  stands  at  the  same  height  as  before.  The  globe, 
now  filled  with  mercury  and  powder,  is  again  detached  and  weighed. 
With  the  difference  of  the  two  weights  we  may  arrive  at  the 
weight  of  the  mercury  whose  volume  is  equal  to  that  of  the  powder, 
in  the  following  manner. 

Let  w   be  the  weight  of  the  powder, 

P  the  weight  of  the  vessel  filled  with  mercury, 
P'  the  weight  of  the  vessel  filled  with  mercury  and  powder, 
D  the  density  of  the  mercury,  about  13.56, 
d    the  density  of  the  powder. 
Then  P' —  w  =  the  weight  of  the  mercury  and  vessel  when  the 

latter  is  partially  filled  with  powder, 
P—  (Pf  —  w)  =  the  weight  of  the  volume  of  mercury  displaced 

by  the  powder. 

Since  the  weights  of  equal  volumes  are  proportional  to  the 
densities,  we  have 

w  :  P-P'  +  w  ::  d  :D 
or 

wD 


8  = 


P-P'+w 


The  density  of  charcoal  powders  varies  between  1.68  and 
1.85. 

SMOKELESS  POWDER. — The  nitrocellulose  smokeless  powders 
are  affected  by  mercury;  therefore  if  the  densimeter  is  used  in 
the  determination  of  the  densities  of  these  powders,  water  must 
be  used  in  the  instrument  in  place  of  mercury.  The  density  of 
large  grained  powders  may  be  determined  by  weighing  a  grain 


GUNPOWDERS.  31 

of  the  powder  in  air  and  in  water.  The  difference  of  the  weights 
in  air  and  water  is  the  weight  of  a  volume  of  water  equal  to  the 
volume  of  the  grain.  The  density  is  then  the  weight  in  air  divided 
by  the  difference  of  the  weights. 

The  density  of  smokeless  powders  varies  from  1.55  to  1.58. 


CHAPTER  II. 


MEASUREMENT  OF  VELOCITIES  AND   PRESSURES. 

1 8.  Measurement  of  Velocity.— 
In  measuring  the  velocity  of  a  pro- 
jectile the  time  of  passage  of  the 
projectile  between  two  points,  a 
known  distance  apart,  is  recorded 
by  means  of  a  suitable  instrument. 
The  calculated  velocity  is  the  mean 
velocity  between  the  two  points, 
and  is  considered  as  the  veloc- 
ity midway  between  the  points.  In 
order  that  this  may  be  done  without 
material  error,  the  two  points  must 
be  selected  at  such  a  distance  apart 
in  the  path  of  the  projectile  that  the 
motion  of  the  projectile  between  the 
points  may  be  considered  as  uni- 
formly varying,  and  the  path  a  right 
line. 

Le  Bouleng€  Chronograph. — The 
instrument  generally  employed  for 
measuring  the  time  interval  in  the 
determination  of  velocity  was  in- 
vented by  Captain  Le  Boulenge  of 
the  Belgian  Artillery,  and  is  called 
the  Le  Boulenge  Chronograph.  It 
has  been  modified  and  improved  by 
Captain  Breger  of  the  French  Artil- 

32 


s- 


0 


W^J 


FIG.  4. 


MEASUREMENT  OF   VELOCITIES  AND  PRESSURES.          33 

lery.  The  brass  column,  a  Fig.  4,  supporting  two  electromagnets,  b 
and  c,  is  mounted  on  the  triangular  bedplate  d  which  is  provided  with 
levels  and  leveling  screws.  The  magnet  b  supports  the  long  rod  e, 
called  the  chronometer,  which  is  enveloped  when  in  use  by  a  zinc  or 
copper  tube  /,  called  the  recorder.  A  nut  above  the  recorder,  shown 
in  Fig.  10,  holds  the  recorder  fixed  in  place  on  the  chronometer  rod. 
The  magnet  c  which  supports  the  short  rod  g,  called  the  registrar, 
is  mounted  on  a  frame  which  permits  it  to  be  moved  vertically 
along  the  standard.  Fastened  to  the  base  of  the  standard  is  the 
flat  steel  spring  h  which  carries  at  its  outer  end  the  square  knife  i. 
The  knife  is  held  retracted  or  cocked  by  the  trigger  j  which  is 
acted  upon  by  the  spring  k.  The  chronometer  e  hangs  so  that  one 
element  of  the  enveloping  tube  or  recorder  is  close  to  the  knife. 
When  the  knife  is  released  by  pressure  on  the  trigger  it  flies  out 
under  the  action  of  the  spring  h  and  indents  the  recorder.  The 
registrar  g  hangs  immediately  over  the  trigger.  When  the  electric 
circuit  through  the  registrar  magnet  is  broken  the  registrar  falls 
on  the  trigger  and  releases  the  knife.  The  tube  I  supports  the 
registrar  after  it  has  fallen  through  it.  Adjustable  guides  are 
provided  to  limit  the  swing  of  the  two  rods  when  first  suspended. 
The  stand  or  table  on  which  the  instrument  is  mounted  is  pro- 
vided with  a  pocket  which  receives  the  chronometer  when  it 
falls,  at  the  breaking  of  the  circuit  that  actuates  its  magnet. 
A  quantity  of  beans  in  the  bottom  of  the  pocket  arrests  the  fall 
of  the  chronometer  without  shock. 

In  the  use  of  the  chronograph  in  measuring  the  velocity  of 
a  shot  the  following  accessory  apparatus  is  required:  targets, 
rheostats,  disjunctor,  and  measuring  rule. 

Targets. — Two  wire  targets,  each  made  of  a  continuous  wire, 
Fig.  5,  are  erected  in  the  path  of  the  projectile.  The  targets 
form  parts  of  electric  circuits  which  include  the  electromagnets 
of  the  chronograph.  Each  magnet  has  its  own  target  and  its 
own  circuit  independent  of  the  other.  The  circuit  from  the  nearer 
or  first  target  includes  the  chronometer  magnet;  the  circuit  from 


34 


ORDNANCE  AND  GUNNERY. 


O    ^-9  7~9 

>~o  o-o    c 

O    '  i  o-o  o-J 

I     > 

FIG.  5. 


the  second  target  includes  the  registrar  magnet.  On  the  passage 
of  the  projectile  through  the  first  target  the  circuit 
is  broken,  the  chronometer  magnet  demagnetized, 
and  the  long  rod,  or  chronometer,  falls.  When  the 
projectile  breaks  the  circuit  through  the  second  tar- 
get the  short  rod,  or  registrar,  falls  and,  striking 
the  trigger,  releases  the  knife,  which  flies  out  and 
marks  the  recorder  at  the  point  which  has  been 
brought  opposite  the  knife  by  the  fall  of  the  chro- 
nometer. 

In  some  instruments  the  chronometer  circuit  is 
led  through  a  contact  piece  not  shown,  carried  by  the  spring  h, 
and  so  arranged  that  the  chronometer  circuit  cannot  be  closed 
until  the  knife  is  cocked.  This  arrangement  prevents  the  loss  of 
a  record  through  failure  to  cock  the  knife  when  suspending  the 
rods  before  the  piece  is  fired. 

The  first  target  must  always  be  erected  at  such  a  distance 
from  the  gun  that  it  will  not  be  affected  by  the  blast.  For  small 
arms  it  is  placed  three  feet  from  the  muzzle  and  consists  of  fine 
copper  wire  wound  backward  and  forward  over  pins  very  close 
together.  For  cannon  it  is  placed  from  50  to  150  feet  from  the 
muzzle,  depending  upon  the  size  of  the  gun.  For  the  measure- 
ment of  ordinary  velocities  the  targets  are  usually  placed  100 
feet  apart  for  small  arms  and  150  feet  for  cannon. 

The  second  target  for  small  arms  consists  of  a  steel  plate  to 
stop  the  bullets,  having  mounted  on  its  rear  face,  and  insulated 
from  it  by  the  block  w,  Fig.  6, 
a  contact  spring  s,  contact  pin  p, 
and  their  binding  screws.  When 
the  bullet  strikes  the  plate  the 
shock  causes  the  end  of  the  spring 
to  leave  the  pin,  and  thus  breaks 
the  circuit,  which  is  immediately  reestablished  by  the  reaction  of 
the  spring.  By  means  of  this  device  constant  repairing  of  the 
target  is  avoided. 


w 

FIG.  6. 


MEASUREMENT  OF  VELOCITIES    AND  PRESSURES. 


35 


19.  The  Rheostat. — Both  circuits  are  led  independently 
through  rheostats,  by  means  of  which  the  resistance  in  the  cir- 
cuits may  be  regulated,  and  the 
strength  of  the  currents  through 
the  two  magnets  equalized.  One 
form  of  rheostat  is  shown  in 
Fig.  7.  The  current  passes  through 
the  contact  spring  a  and  through 
a  German  silver  wire  wound  in 
grooves  on  the  wooden  drum  6. 
By  turning  the  thumb  nut  c  the 
contact  spring  is  shifted,  and  more 
or  less  of  the  wire  is  included  in 
the  circuit. 

Another     form     of     rheostat; 

through  which  both  circuits  pass 

.  FIG.  7. 

independently,  is  shown  in  Fig.  8. 

Each  current  passes  through  a  strip  of  graphite,  a,  and  the  resist- 
ance in  the  circuit  may  be  increased  or  diminished  by  sliding  the 


contact  piece  6  so  as  to  include  a  greater  or  less  length  of  the 
graphite  strip  in  the  circuit. 

The  Disjunctor. — Both  circuits  also  pass  independently  through 
an  instrument  called  the  disjunctor,  by  means  of  which  they  may 
be  broken  simultaneously.  The  disjunctor  is  shown  in  elevation 
and  part  section  in  Fig.  9.  The  two  halves  of  the  instrument  are 
exactly  similar.  The  two  contact  springs  c,  weighted  at  their 
free  ends,  bear  against  insulated  contact  pins  e,  supported  in  the 
same  metal  frame  d.  The  frame  is  pressed  upward  against  the 


36 


ORDNANCE  AND  GUNNERY. 


spring  catch  h  by  two  other  contact  springs,  /.  The  electric  cir- 
cuit passes  from  one  binding  post  through  the  parts  /,  e,  c,  and  a 
to  the  other  binding  post. 

On  the  release  of  the  spring  catch  h  the  frame  d  flies  upward 
under  the  action  of  the  springs  /  until  stopped  by  the  pin  g. 


FIG.  9. 

At  the  sudden  stoppage  of  the  movement  the  weighted  ends  of 
the  contact  springs  simultaneously  leave  the  contact  pins,  thus 
breaking  both  circuits  momentarily.  Mounted  on  a  shaft  are  two 
hard  rubber  cams,  b,  which  bear  against  other  springs,  a,  in  the 
two  circuits.  On  turning  the  cam  shaft  the  connection  between 
the  parts  a  and  c  is  broken,  breaking  both  electric  circuits,  but 
not  necessarily  simultaneously.  The  circuits  are  habitually 
broken  in  this  manner  except  when  taking  disjunction  or  records 
in  firing. 

20.  Disjunction. — By  means  of  the  disjunctor  both  circuits 
-are  broken  at  the  same  instant.  The  mark  made  by  the  knife 
under  these  circumstances  is  called  the  disjunction  mark,  and  its 
height  above  a  zero  mark  made  by  the  knife  when  the  chronometer 
is  suspended  from  its  magnet  is  evidently  the  height  through  which 
a  free  falling  body  moves  in  the  time  used  by  the  instrument  hi 
making  a  record.  This  time  includes  any  difference  in  the  times 
required  for  demagnetization  of  the  two  magnets,  the  time  occu- 


MEASUREMENT  OF  VELOCITIES  AND  PRESSURES.          37 

pied  by  the  registrar  in  falling,  and  the  time  required  for  the 
knife  to  act. 

From  the  height  as  measured  we  obtain  the  corresponding 
time  from  the  law  of  falling  bodies, 


Now  when  the  circuits  are  broken  by  the  projectile  the  chro- 
nometer begins  to  fall  before  the  registrar.  The  mark  made  by 
the  knife  will  therefore  be  found  above  the  disjunction  mark.  If 
we  measure  the  height  of  this  second  mark  above  the  zero,  the 
corresponding  time  is  the  whole  time  that  the  chronometer  was 
falling  before  the  mark  was  made,  and  to  obtain  the  time  between 
the  breaking  of  the  circuits  we  must  subtract  from  this  time  the 
time  used  by  the  instrument  in  making  a  record,  or  the  time  cor- 
responding to  the  disjunction.  Let  hi  and  h2  represent  the  heights 
of  the  disjunction  and  record  marks  respectively,  ti  and  t2  the 
corresponding  times.  Let  t  be  the  time  between  the  breaking  of 
screens,  then 


It  will  be  seen  by  the  equation  that  the  difference  of  the  times,  and 
not  the  difference  of  the  heights,  must  be  taken. 

FIXED  DISJUNCTION.  —  For  the  velocity  at  the  middle  point 
between  targets  we  have,  representing  by  s  the  distance  between 
the  targets,  % 

v  =  s/t 

Substituting  for  t  its  value,  we  have 


From  this  equation  we  see  that  if  the  value  of  s,  and  of  (2hi/g)* 
the  disjunction,  be  fixed,  the  values  of  v  can  be  calculated  for 
all  values  of  h2  within  the  limits  of  practice,  and  tabulated.  This 
has  been  done  for  the  values  s  =  100  feet  and  (2/&i/gr)*  =  0.15  sec- 


38 


ORDNANCE  AXD  GUNNERY. 


-s 


-S 


FIG.  10. 


onds.  This  value  of  (2/ii/gr)*  is  called  $e  /kred  dzs- 
junction.  If  such  a  table  is  not  at  hand,  the  fixed 
value  of  the  disjunction  avoids  the  labor  of  calculating 
(2/ii/gr)*  for  each  shot. 

In  this  case 

<  =  <2-0.15  sec.  =  (2A2/gr)i- 0.15. 

In  ordinary  practice  it  is  better  to  take  the  disjunc- 
tion at  each  shot,  and  to  keep  the  disjunction  mark 
near  the  disjunction  circle,  but  not  necessarily  on  it. 
The  times  corresponding  to  the  heights  of  the  disjunc- 
tion and  record  marks  are  both  read  from  the  table,  and 
with  the  difference  of  these  times  the  velocity  is  taken 
from  another  table. 

Measuring  Rule. — For  measuring  the  height  of  the 
mark  on  the  recorder  above  the  zero  mark  there  is  pro- 
vided with  the  instrument  a  rule  graduated  in  milli- 
meters, and  with  a  sliding  index  and  vernier,  the  least 
reading  being  ^  of  a  millimeter.  The  swivelled  pin  at 
the  end  of  the  rule,  Fig.  10,  is  inserted  in  the  hole  through 
the  bob  of  the  chronometer,  and  the  knife  edge  of  the 
index  is  placed  at  the  lower  edge  of  the  mark  whose 
height  is  to  be  measured.  The  height  is  then  read  from 
the  scale.  Tables  are  constructed  from  which  can  be 
directly  read  the  time  corresponding  to  any  height  in 
millimeters  within  the  limits  o£  the  scale.  The  maxi- 
mum time  that  can  be  measured  with  this  chronograph 
is  limited  by  the  length  of  the  chronometer  rod,  and  is 
about  0.15  of  a  second. 

21.  Adjustments  and  Use. — The  instrument  must 
be  properly  mounted  on  a  stand  at  such  a  distance  from 
the  gun  that  it  will  not  be  affected  by  the  shock  of  dis- 
charge. The  electrical  connections  with  the  batteries 
and  targets,  through  the  rheostats  r  and  disjunctor  d, 
are  made  as  shown  in  Fig.  11. 

To  adjust  the  instrument,  first  level  it  by  the  level- 


MEASUREMENT  OF  VELOCITIES  AND  PRESSURES. 


39 


ing  screws,  cock  the  knife,  and  suspend  the  chronometer  rod,  en- 
veloped by  the  recorder,  from  its  magnet.  See  that  the  recorder 
hangs  close  to  the  knife  and  that  no  part  of  the  base  of  the  rod 
touches  any  part  of  the  instrument.  The  guides  must  be  close  to. 
but  not  touching,  the  bob  of  the  chronometer.  Depress  the 


FIG.  11. 

trigger.  The  knife  will  mark  the  recorder  near  the  bottom.  This 
mark  is  the  zero  from  which  all  heights  are  measured,  and  the 
knife  edge  on  the  measuring  rule  index  must  be  so  adjusted  that 
the  zero  of  the  vernier  shall  coincide  with  the  zero  of  the  scale 
when  the  knife  edge  is  in  the  mark.  The  adjustment  of  the  knife 
is  made  as  follows.  Place  the  sliding  index  so  that  the  zero  of  the 
vernier  is  at  the  zero  of  the  scale  on  the  rule.  Clsmp  the  index 
and  apply  the  rule  to  the  chronometer.  Loosen  the  screws  that 
hold  the  knife  and  adjust  the  knife  edge  to  the  zero  mark  on  the 
recorder.  Tighten  the  knife  screws.  After  this  adjustment, 
slide  the  index  to  the  mark  Disjunction  on  the  rule,  and  letting 
the  knife  edge  bear  against  the  recorder  turn  the  recorder  around 
the  chronometer  rod.  The  knife  edge  will  scribe  a  circle  on  the 
recorder,  and  the  mark  made  at  disjunction  should  fall  on  or  near 
this  circle. 


40  ORDNANCE  AND  GUNNERY. 

To  regulate  the  strength  of  the  magnets  each  of  the  rods  is 
provided  with  a  tubular  weight,  one  tenth  that  of  the  rod.  Place 
the  proper  weight  on  each  rod  and  suspend  the  rods  from  their 
magnets.  Increase  the  resistance  in  each  circuit  by  slowly  mov- 
ing the  contact  piece  of  the  rheostat  until  the  rod  falls.  Remove 
the  weights  from  the  rods  and  again  suspend  the  rods.  Take 
the  disjunction.  If  the  bottom  of  the  mark  made  by  the  knife 
does  not  lie  on  or  near  the  circle  previously  scribed  on  the  recorder, 
raise  or  lower  the  registrar  magnet  until  coincidence  is  nearly 
obtained. 

Test  the  disjunctor  by  shifting  the  two  circuits.  The  height 
of  disjunction  should  remain  the  same. 

Test  the  circuits  by  suspending  the  rods  and  causing  the 
circuits  to  be  broken  successively  at  the  two  targets.  Note  that 
the  proper  rod  falls  as  each  circuit  is  broken. 

Always  suspend  the  chronometer  rod  with  the  same  side  of 
the  bob  to  the  front,  and  always,  before  suspending  it,  press 
the  recorder  hard  against  the  bob.  After  each  record  turn  the 
recorder  slightly  on  the  rod  to  present  a  new  element  to  the  knife. 

Circuits  should  always  be  broken  at  the  disjunctor  when 
the  rods  are  not  actually  suspended,  and  the  rods  should  be 
allowed  to  remain  suspended  as  short  a  time  as  possible. 

Measurement  of  Very  Small  Intervals  of  Time. — For  the 
measurement  of  very  small  time  intervals  the  registrar  mag- 
net is  raised  to  near  the  top  of  the  standard  and  placed  in  the 
circuit  with  the  first  target.  The  chronometer  magnet  is  put 
in  the  circuit  with  the  second  target.  Under  this  arrangement 
the  disjunction  mark  will  be  made  near  the  top  of  the  recorder 
and  the  record  mark  under  the  disjunction.  The  interval  of 
time  measured  is  obtained  by  subtracting  the  time  corresponding 
to  the  height  of  the  record  mark,  from  the  tune  of  disjunction. 
The  object  of  this  arrangement  is  to  obtain  the  record  when  the 
chronometer  has  acquired  a  considerable  velocity  of  fall,  so  that 
the  scale  of  time  will  be  extended,  and  small  errors  of  reading 
will  not  produce  large  errors  in  time. 


MEASUREMENT  OF  VELOCITIES  AND  PRESSURES. 


41 


22.  Schultz  Chronoscope. — The  Le  Boulenge  chronograph 
measures  a  single  time  interval  only.  When  it  is  desired  to 
measure  the  intervals  between  several  successive  events  an  instru- 
ment that  provides  a  more  extensive  time  scale  is  required. 

The  Schultz  Chronoscope  is  an  instrument  of  this  class.  An 
electrically  sustained  tuning  fork,  c,  Fig.  12,  whose  rate  of  vibra- 
tion is  known,  carries  on  one  tine  a  quill  point  b  which  bears 
against  the  blackened  surface  of  the  revolving  cylinder  a  and 
marks  on  it  a  sinusoidal  curve  which  is  the  scale  of  time.  By 


FIG.  12. 


FIG.  13. 


giving  motion  of  translation  to  the  cylinder  past  the  fork  the 
time  scale  may  be  extended  helically  over  the  whole  length  of 
the  cylinder.  The  records  of  events,  such  as  the  passage  of  the 
shot  through  screens,  are  made  by  the  breaking  of  successive 
circuits  which  pass  through  the  Marcel  Deprez  registers  shown 
at  e,  Fig.  12,  and  in  Fig.  13.  When  the  circuit  is  broken  the 
magnet  e,  Fig.  13,  is  demagnetized,  and  the  spring  g  rotates  the 
armature  /  and  the  quill  h  attached  to  it.  This  marks  a  bend 
or  offset  in  the  trace  of  the  quill  on  the  revolving  cylinder,  and 
the  point  of  the  bend  referred  to  the  time  scale  marks  the  instant 
of  the  breaking  of  the  circuit. 


42 


ORDNANCE  AND  GUNNERY. 


It  will  be  noted  that  the  tuning  fork  has  a  constant  lead  with 
respect  to  any  register.  The  point  of  the  time  scale  that  corre- 
sponds to  any  point  on  a  register  record  is  found  at  the  length  of 
this  lead  from  the  point  on  the  time  scale  opposite  the  given  point 
on  the  register  record. 

The  Sebert  Velocimeter. — This  instrument  is  used  to  record 
the  movement  of  the  gun  in  recoil.  A  blackened  steel  ribbon,  S, 


T 

-A 


-r 


FIG.  14. 

Fig.  14,  is  attached  by  the  wire  T  to  a  bolt  projecting  from  the 
trunnion  of  the  gun.  As  the  gun  recoils  it  pulls  the  ribbon  past 
the  registers  R  and  the  tuning  fork  A,  whose  rate 
of  vibration  is  known.  The  quill  on  the  tuning 
fork  marks  the  time  scale  on  the  blackened  rib- 
bon as  shown  by  the  curve  t,  Fig.  15.  The  tune 
occupied  by  the  gun  in  traversing  any  length  is 
obtained  by  laying  off  this  length  on  the  time 
scale  and  counting  the  vibrations  and  parts  of  a 
vibration  included.  The  right  line  through  the 
centre  of  the  time  scale  is  made  by  pulling  the 
ribbon  past  the  fork  when  the  fork  is  not  vibrating. 
FIG.  15.  The  line  assists  in  the  count  of  the  number  of 

double  vibrations  in  any  length. 

The  time  scale  is  therefore  a  complete  record  of  the  move- 
ment of  the  gun;  and  by  measuring  from  it  the  length  travelled 
by  the  gun  during  any  vibration  of  the  fork  the  velocity  of  the 
gun  at  the  middle  instant  of  the  vibration  may  be  determined. 


MEASUREMENT  OF   VELOCITIES  AND  PRESSURES.          43 

When  the  gun  moves  in  free  recoil,  that  is,  when  it  is  so  mounted 
that  it  recoils  horizontally  and  with  very  little  friction,  the  ve- 
locities of  the  projectile  may  be  determined  from  the  velocities 
of  the  gun;  and  the  pressures  necessary  to  produce  these  veloci- 
ties hi  the  projectile  may  then  be  determined. 

The  registers  have  no  function  in  the  measurement  of  the 
recoil  proper,  but  may  be  used  to  record  any  event  happening 
while  the  recoil  record  is  being  made.  The  instant  of  the  de- 
parture of  the  projectile  from  the  bore  is  usually  thus  recorded, 
and  independent  measurement  of  the  velocity  of  the  projectile 
between  points  in  the  bore  may  also  be  made. 

Two  register  records  are  shown  by  the  lines  r,  Fig.  15,  the 
event  recorded  by  each  register  having  occurred  when  the  offset 
at  s  was  made.  The  time  that  elapsed  between  the  beginning 
of  movement  and  the  occurrence  of  the  event  recorded  is  obtained 
by  laying  off  on  the  time  scale  the  length  from  the  origin  of  the 
register  record  to  the  offset. 

Methods  of  Measuring  Interior  Velocities. — Two  methods 
that  have  been  used  in  determining  the  instant  of  the  projec- 


FIG.  16. 


tile's  passage  past  selected  points  in  the  bore  are  shown  in  Figs.  16 
and  17. 


M    i 

f€I 

BREECH 

1  1 

1  1 

'•';5$-"3                                   ^*\ 

'.        -             ••"•K:~3                                      Jf 

*  jf    *ti 

FIG.  17. 


Some  circuit  breaking  device  is  used  at  the  points  selected, 
and  the  electric  wires  are  led  to  any  suitable  velocity  instru- 
ment. 


44  ORDNANCE  AND  GUNNERY. 

23.  Measurement  of  Pressures. — Pressures  in  cannon  are  di- 
rectly measured  by  means  of  the  pressure  gauge  shown  in  Fig.  18. 
In  the  steel  housing  h  are  assembled  the  steel  piston  p  and  the 
copper  cylinder  c,  which  is  centered  by  the  steel  spring  or  rubber 
washer  w.      The  housing  is  closed  by  the  screw 
plug  s.     A  small  copper  obturating  cup  o  pre- 
vents the  entrance  of  gas  past  the  piston,  and 
a  copper  washer  performs  the  same  office  at 
the  joint  between  the  housing  and  the  closing 
plug.     A  series  of  grooves  a,  called  air  packing, 
is  sometimes  cut  near  the  bottom  of  the  piston, 
and  assists  in  obturation  in  the  case  of  a  defect 
in  the  copper  cup.     Any  gas  that  may  pass 
the  cup  has  its  tension  materially  reduced  by  expansion  into  the 
successive  grooves. 

In  another  form  of  gauge  the  housing  is  threaded  on  the 
exterior  and  the  gauge  is  screwed  into  a  socket  provided  in  the 
head  of  the  breech  block. 

The  gauge  is  placed  in  the  gun  behind  the  powder  charge, 
or  is  inserted  in  its  socket  in  the  breech  block.  When  the  gun 
is  fired  the  pressure  of  the  powder  gases  is  exerted  against  the 
end  of  the  piston  and  the  copper  cylinder  is  compressed.  The 
compression  is  manifestly  due  to  the  maximum  pressure  exerted 
in  the  gun.  The  length  of  the  cylinder  is  measured  both  before 
and  after  firing,  and  the  compression  due  to  the  pressure  is  deter- 
mined. With  the  compression  thus  obtained  the  pressure  per 
square  inch  that  produced  it  is  read  at  once  from  a  tarage  table 
previously  constructed. 

The  Tarage  Table. — The  copper  cylinders  are  cut  in  half- 
inch  lengths  from  rods  very  uniformly  rolled  and  carefully  an- 
nealed. The  compression  of  the  cylinders  under  different  loads 
is  determined  in  a  static  pressure  machine.  It  is  assumed  that 
the  compression  obtained  in  firing  is  due  to  a  load  on  the  piston 
of  the  pressure  gauge  equal  to  the  load  that  produced  the  same 
compression  in  the  static  machine.  The  pressure  per  square 


MEASUREMENT  OF  VELOCITIES  AND  PRESSURES.          45 

inch  in  the  gun  may  therefore  be  obtained  by  dividing  the  static 
load  that  corresponds  to  the  observed  compression  by  the  area 
of  the  piston  in  the  pressure  gauge.  Knowing  the  area  of  the 
piston  used,  the  table  of  compressions  and  corresponding  pres- 
sures per  square  inch  is  readily  constructed  from  the  results 
obtained  in  the  machine. 

The  area  of  piston  in  cannon  gauges  is  Vio  of  a  square 
inch,  and  in  the  small-arm  pressure  barrel,  1/30  of  a  square 
inch. 

Initial  Compression. — When  the  pressure  in  the  gun  is  high 
the  compression  of  the  copper  is  considerable,  and  the  piston 
acquires  an  appreciable  velocity  during  the  compression.  The 
energy  of  the  piston  due  to  this  velocity  adds  to  the  compres- 
sion that  would  result  from  the  pressure  alone,  and  consequently 
the  measured  compression  is  greater  than  the  compression  that 
corresponds  to  the  true  pressure.  The  energy  of  the  piston 
may  be  reduced  in  two  ways:  by  reducing  its  weight,  and  by 
limiting  its  travel  and  accompanying  velocity.  The  piston  is 
made  as  light  as  possible  consistent  with  the  duty  it  has  to  per- 
form. To  limit  its  travel  the  copper  cylinders  are  initially  com- 
pressed before  using,  by  a  load  corresponding  to  a  pressure 
somewhat  less  than  that  expected  in  the  gun.  Further  com- 
pression of  the  copper  will  not  occur  until  the  load  applied  in  the 
gun  is  close  to  that  used  in  the  initial  compression. 

The  general  practice  is  to  use  a  copper  initially  compressed 
by  a  load  corresponding  to  a  pressure  about  3000  Ibs.  less  than 
that  expected  in  the  gun.  Thus  if  a  pressure  of  35,000  Ibs.  is 
expected,  a  copper  initially  compressed  by  a  load  correspond- 
ing to  32,000  Ibs.  per  square  inch  is  used. 

Small-arm  Pressure  Barrel. — In  the  measurement  of  pres- 
sures in  small  arms  a  specially  constructed  barrel  whose  bore 
is  the  same  as  that  of  the  rifle  barrel  is  used.  The  piston  of  the 
pressure  gauge  passes  through  a  hole  bored  through  the  barrel 
over  the  chamber,  and  a  steel  housing  erected  over  this  part  of 
the  barrel  serves  as  an  anvil  for  the  copper  cylinder. 


46 


ORDNANCE  AND  GUNNERY. 


A  hole  is  bored  through  the  metallic  cartridge  case  to  per- 
mit the  powder  gases  to  act  directly  on  the  end  of  the 
piston. 

24.  The  Micrometer  Caliper. — The  micrometer  caliper,  Fig. 
19,  is  used  for  measuring  the  lengths  of  the  copper  cylinders 
before  and  after  firing.  This  instrument  is  used  generally  for  the 
measurement  of  short  exterior  lengths. 


FIG.  19. 


The  movable  measuring  point  p  has  a  screw  thread  of  forty 
turns  to  the  inch  cut  on  its  shaft.  One  turn  of  the  attached 
micrometer  head  m  therefore  moves  the  point  one  fortieth  or 
25  thousandths  of  an  inch.  By  means  of  the  scale  on  the 
spindle  and  the  25  divisions  on  the  micrometer  head  m  the  dis- 
tance that  separates  the  measuring  points  can  be  read  to  the 
one-thousandth  of  an  inch,  and  by  further  subdividing  the  divi- 
sions on  the  head  by  the  eye,  readings  to  the  ten-thousandth  of 
an  inch  may  be  made..  The  figure  represents  the  points  as  sepa 
rated  by  0.2907  inches. 

The  Dynamic  Method  of  Measuring  Pressures. — This  con 
sists  in  determining  the  velocities  of  the  gun  in  recoil,  as  by  the 
Sebert  velocimeter,  or  of  the  shot  at  different  points  of  the  bore. 
The  differences  of  the  velocities  divided  by  the  corresponding 
differences  of  the  times  give  the  accelerations,  and  the  corre- 
sponding pressures  are  obtained  by  multiplying  the  accelera- 
tions by  the  mass.  A  pressure  obtained  in  this  manner  is 
evidently  only  the  pressure  required  to  produce  the  observed 


MEASUREMENT  OF  VELOCITIES  AND  PRESSURES.          47 

acceleration  in  a  body  whose  mass  is  that  of  the  gun  or  of 
the  projectile.  That  part  of  the  pressure  expended  in  over- 
coming the  friction  of  the  projectile  in  the  bore  and  in  giving 
rotation  to  the  projectile  is  neglected.  The  measured  pressure 
is  consequently  less  than  the  true  pressure  exerted  in  the 
gun. 

Comparison  of  the  Two  Methods. — When  the  same  pressure 
in  the  bore  is  measured  by  the  dynamic  method  and  by  the  pres- 
sure gauge  the  result  obtained  dynamically  is  usually  the  greater, 
and  this  notwithstanding  the  fact,  as  just  explained,  that  the 
dynamically  measured  pressure  is  less  than  the  true  pressure. 
This  causes  doubt  as  to  the  correctness  of  the  pressures  recorded 
by  the  gauge. 

In  the  gun  the  compression  of  the  copper  is  effected  in  a  very 
small  fraction  of  the  time  required  in  the  static  machine  that 
produced  the  tarage,  and  as  the  maximum  pressure  in  the  gun 
is  instantly  relieved,  it  is  held  that  the  metal  of  the  copper  cylinder 
has  not  time  to  flow  under  this  pressure,  and  consequently  that 
the  compression  is  less  than  it  would  be  under  the  same  load 
in  the  static  machine.  The  pressure  as  obtained  from  the  com- 
pression in  the  gauge  is  therefore  less  than  the  true  pressure  in 
the  gun. 

On  the  other  hand  Sarrau,  an  eminent  French  investigator, 
concludes  from  many  experiments  that  with  gunpowder,  when 
the  pressure  gauge  is  placed  in  rear  of  the  projectile,  the  com- 
pressions will  agree  with  the  tarage.  The  maximum  pressure 
in  the  gun  is  reached  in  a  very  short  time,  but  the  time  is  appre- 
ciable. Therefore  the  application  of  the  pressure  resembles  in 
some  degree  that  of  the  force  producing  the  tarage.  When 
high  explosives  are  used,  or  when  with  gunpowder  the  pressure 
gauge  is  placed  anywhere  in  front  of  the  base  of  the  projectile  so 
that  the  gas  strikes  it  suddenly  upon  the  passage  of  the  projectile, 
the  rate  of  application  of  the  force  is  so  great  that  as  a  general 
rule  the  true  pressure  is  measured  by  the  tarage  corresponding  to 
half  the  actual  compression  of  the  cylinder. 


48  ORDNANCE  AND  GUNNERY. 

Though  these  differences  of  opinion  as  to  the  correctness  of  the 
pressure  gauge  exist,  the  gauge  itself  is  in  general  use.  It  affords 
the  most  convenient  method  of  getting  a  measure  of  pressure,  and 
serves  to  compare  the  measured  pressure  with  what  is  known 
from  experience  to  be  a  safe  pressure  in  the  gun. 


CHAPTER  III. 
INTERIOR  BALLISTICS. 

25.  Scope. — Ballistics  is  the  science  that  treats  of  the  motion 
of  projectiles. 

Interior  ballistics  is  concerned  with  the  motion  of  the  projectile 
while  in  the  bore  of  the  gun,  and  includes  a  study  of  the  condi- 
tions existing  in  the  bore  from  the  moment  of  ignition  of  the 
powder  charge  to  the  moment  that  the  projectile  leaves  the  muz- 
zle. The  circumstances  attending  the  combustion  of  the  powder, 
the  pressures  exerted  by  the  gases  at  different  points  of  the  bore, 
and  the  velocities  impressed  upon  the  projectile  are  the  subjects 
of  investigation;  and  the  practical  results  of  the  study  lie  in  the 
application  of  the  deduced  mathematical  formulas  which  connect 
the  travel  of  the  projectile  with  the  velocities  and  pressures.  By 
means  of  the  formulas  we  may  determine  the  stresses  to  which  a 
gun  is  subjected  from  the  pressure  of  the  powder  gases,  and  the 
dimensions  of  chamber  and  of  bore,  and  the  weight  of  powder,  to 
produce  in  a  given  projectile  a  desired  velocity.  The  action  of 
different  powders  may  be  compared  and  the  most  suitable  powder 
selected  for  a- particular  gun.  The  interior  pressures  at  all  points 
along  the  bore  being  made  known,  the  thickness  required  in  the 
walls  of  the  gun  to  safely  withstand  these  pressures  are  deter- 
mined from  the  principles  of  gun  construction,  to  be  studied 
later. 

Early  Investigations. — In  1743  Benjamin  Robins  described, 
before  the  Royal  Society  of  England,  experiments  that  he  had 
made  to  determine  the  velocities  of  musket  balls  when  fired  with 

49 


50  ORDNANCE  AND  GUNNERY. 

given  charges  of  powder.  To  measure  the  velocities  he  invented 
the  ballistic  pendulum,  which  consisted  simply  of  a  large  block  of 
wood  suspended  so  as  to  move  freely.  The  bullet  was  fired  into 
the  block  of  wood',  and  the  velocity  impressed  upon  the  pendulum 
was  measured.  By  equating  the  expressions  for  the  quantities 
of  motion  in  the  bullet  before  striking  the  pendulum,  and  in  the 
pendulum  after  receiving  the  bullet,  the  velocity  of  the  bullet  was 
obtained.  The  gun  pendulum,  which  consisted  of  a  gun  rriounted 
to  swing  as  a  pendulum,  was  also  invented  by  Robins.  Among 
other  deductions  made  from  his  experiments  Robins  announced 
the  following.  The  temperature  of  explosion  is  at  least  equal  to 
that  of  red-hot  iron;  the  maximum  pressure  exerted  by  the  powder 
gases  is  equal  to  about  1000  atmospheres;  the  weight  of  the  per- 
manent gases  is  about  three  tenths  that  of  the  powder,  and  their 
volume  at  atmospheric  temperature  and  pressure  about  240  times 
that  occupied  by  the  charge. 

Dr.  Charles  Hutton,  Professor  in  the  Royal  Military  Academy , 
Woolwich,  continued  Robins's  experiments,  1773  to  1791,  improv- 
ing and  enlarging  the  ballistic  pendulum  so  that  it  could  receive 
the  impact  of  one-pound  balls.  He  verified  Robins's  deductions 
as  to  the  nature  of  the  gases,  but  put  the  temperature  of  explosion 
at  double  that  previously  deduced,  and  the  maximum  pressure  at 
2000  atmospheres.  Hutton  produced  a  formula  for  the  velocity 
of  a  spherical  projectile  at  any  point  of  the  bore,  upon  the  assump- 
tion that  the  'combustion  of  the  charge  is  instantaneous  and  that 
the  expansion  of  the  gas  follows  Mariotte's  law, — no  account 
being  taken  of  the  loss  of  heat  due  to  work  performed — a  principle 
which,  at  that  time,  was  unknown. 

In  1760  the  Chevalier  D'Arcy  made  the  first  attempt  to  deter- 
mine dynamically  the  law  of  pressure  in  the  bore  by  successively 
shortening  the  length  of  the  barrel  and  measuring  the  velocity  of 
the  bullet  for  each  length.  The  pressures  were  determined  from 
the  calculated  accelerations. 

In  1792  Count  Rumford,  born  in  the  United  States,  endeavored 
to  make  direct  measurement  of  the  pressure  exerted  by  fired  gun- 


INTERIOR  BALLISTICS.  51 

powder  by  measuring  the  maximum  weights  lifted  by  different 
charges  fired  in  a  small  but  very  strong  wrought  iron  mortar,  or 
eprouvette.  He  determined  a  relation  existing  between  the  pres- 
sure of  the  powder  gases  and  their  density.  The  maximum  pres- 
sure that  would  be  exerted  by  the  gases  from  a  charge  that  com- 
pletely filled  the  chamber  was,  as  calculated  by  Rumford,  about 
100  tons  to  the  square  inch.  Noble  and  Abel,  in  their  later 
experiments,  arrived  at  43  tons  per  square  inch  as  the  maximum 
pressure  under  these  conditions.  Their  value  is  now  accepted  as 
being  very  near  the  truth.  The  great  difference  in  the  two  deter- 
minations is  probably  due  to  the  fact  that  Rumford  deduced  his 
value  for  the  maximum  pressure  from  experiments  with  small 
charges  that  did  not  fill  the  chamber,  so  that  the  energy  of  the 
gases  was  greatly  increased  by  the  high  velocity  they  attained 
before  acting  on  the  projectile. 

Later  Investigations. — In  the  years  1857  to  1860  General  Rod- 
man of  the  Ordnance  Department,  United  States  Army,  conducted 
the  experiments  that  resulted  in  the  change  of  form  of  powder 
grains  and  their  variation  in  size  according  to  the  caliber  of  the 
gun.  He  devised  the  pressure  gauge  for  directly  measuring  the 
maximum  pressures  of  the  powder  gases.  His  gauge  differed  from 
the  pressure  gauge  now  in  use,  only  in  the  method  employed  to 
record  the  pressure.  The  piston  of  the  gauge  carried  at  its  inner 
end  a  V-shaped  knife,  and  the  amount  of  the  pressure  was  read 
from  the  length  of  the  cut  made  by  the  knife  in  a  disk  of  copper. 
General  Rodman  was  also  the  author  of  the  principle  of  interior 
cooling  of  cast  iron  cannon,  by  the  application  of  which  principle 
the  metal  surrounding  the  bore  of  a  gun  was  put  under  a  perma- 
nent compressive  strain  which  greatly  increased  the  resistance  of 
the  gun  to  the  interior  pressures. 

In  1874  Noble  and  Abel  announced  the  results  of  their  experi- 
ments on  the  explosion  of  gunpowder  in  closed  vessels.  As  the 
ballistic  formulas  now  in  use  are  based  largely  on  the  results  of 
Noble  and  Abel's  experiments,  these  will  later  be  more  fully 
described. 


52  ORDNANCE  AND  GUNNERY. 

26.  Gravimetric  Density  of  Powder. — The  density  of  powder 
is,  as  has  been  explained  on  page  29,  the  ratio  of  the  weight  of  a 
given  volume  of  powder  to  the  weight  of  an  equal  volume  of 
water.  In  determining  density  the  volume  considered  is  the 
volume  actually  occupied  by  solid  powder. 

Gravimetric  Density  is  the  mean  density  of  the  contents  of  the 
volume  that  is  exactly  filled  by  the  powder  charge.  The  air 
spaces  between  the  grains  are  considered  as  well  as  the  solid 
powder  in  the  charge.  The  gravimetric  density  is  obtained  by 
dividing  the  weight  of  the  charge  by  the  weight  of  water  that 
will  fill  the  volume  occupied  by  the  charge.  It  is  evident  that  if 
a  solid  block  of  powder  of  a  given  density  is  broken  up  into  grains, 
the  volume  occupied  by  the  powder  will  increase  and  will  be 
dependent  on  the  form  and  size  of  the  grains.  While  the  actual 
density  of  the  solid  powder  does  not  change,  the  gravimetric  den- 
sity will  depend  upon  the  granulation. 

A  cubic  foot  of  powder  is  usually  taken  in  determining  gravi- 
metric density.  A  cubic  foot  of  water  weighs  62.425  Ibs. 

Let   f  be  the  gravimetric  density  of  the  powder, 

W  the  weight  of  a  cubic  foot  of  powder. 
Then,  by  definition, 

f  =  17/62.425 

If  the  chamber  of  the  gun  were  filled  with  a  solid  cake  of 
powder,  the  value  of  7-  would  be  the  density  of  the  powder.  In 
practice  the  value  of  f  usually  lies  between  0.875  and  1.0,  though 
sometimes  the  value  unity  is  exceeded. 

The  space  actually  occupied  by  the  solid  powder  in  a  given 
volume  is  determined  as  follows. 

Let  V  be  the  total  volume  occupied  by  the  powder, 
v  the  volume  of  the  solid  powder. 

Since  volumes  of  equal  weights  are  inversely  as  the  densities, 
we  have 

V:v::d:r     or     v  =  ^V  (20) 


INTERIOR  BALLISTICS.  53 

It  is  evident  from  this  equation  that  when  the  gravimetric 
density  of  the  powder  is  unity,  the  volume  of  the  solid  powder  is 
equal  to  the  volume  of  the  charge  multiplied  by  the  reciprocal 
of  the  density  of  the  powder. 

If  ^  =  1.00  and  7-  =  1.76  (a  mean  value  for  charcoal  powders), 
we  have 

v  =  .57V  (21) 

That  is,  the  volume  occupied  by  the  solid  powder  in  a  charge  is 
about  .57  of  the  total  volume  of  the  charge. 

27.  Density  of  Loading. — Density  of  loading  is  the  mean  den- 
sity of  the  contents  of  the  whole  powder  chamber.  In  addition 
to  the  solid  powder  and  the  air  spaces  between  the  grains,  the 
space  in  the  chamber  not  occupied  by  the  powder  charge  is  also 
considered.  The  density  of  loading  is  obtained  by  dividing  the 
weight  of  the  charge  by  the  weight  of  water  that  will  fill  the 
powder  chamber. 

Let  J  be  the  density  of  loading, 

at  the  weight  of  the  charge  in  pounds, 
C  the  volume  of  the  chamber  in  cubic  inches. 
Then,   since  one  pound  of  water   occupies  27.68   cubic   inches, 
C/27.68  will  be  the  weight  of  water  that  will  fill  the  chamber,  and 

J  =  CD  -s-  C/27.68  =  27.68d)/C  (22) 

If  instead  of  the  cubic  inch  and  pound  we  use  as  units  the  cubic 
decimeter  and  kilogram,  the  number  of  cubic  decimeters  in  the 
volume  of  the  chamber  will  express  at  once  the  weight  of  water  in 
kilograms  that  will  fill  the  chamber,  since  one  kilogram  of  water 
occupies  a  volume  of  one  cubic  decimeter.  Using  metric  units 
the  above  expression  therefore  becomes 

J  =  d>/C  (23) 

The  density  of  loading  may  also  be  expressed  in  terms  of  the 
density  of  the  powder  as  follows. 


54  ORDNANCE  AND  GUNNERY. 

Let  C"  be  the  volume  in  cubic  inches  occupied  by  the  solid 
powder  of  the  charge;  d  the  density  of  the  powder.  dCf  will 
then  be  the  volume  of  an  equal  weight  of  water,  and 

&  =  dC'/27.G8  (24) 

which,  substituted  in  equation  (22),  gives 

A  =  dC'/C  (25) 

The  accompanying  figure  will  serve  to  illustrate  the  difference 
between  density,  gravimetric  density,  and  density  of  loading.    The 
figure  represents  a  section  of  the  whole  chamber 
of  a  gun  charged  with  powder  to  the  line  A.     The 
density  of  loading  is  in  this  case  the  weight  of 
powder  below  the  line  A  divided  by  the  weight  of 
water  that  will  fill  the  whole  chamber.     The  gravi- 
metric density  is  the  weight  of  the  powder  divided 
by  the  weight  of  water  that  will  fill  all  that  part 
of  the  chamber  below  the  line  A.    Now  consider- 
ing the  powder  charge  as  compressed  into  a  solid  mass  at  the 
bottom  of  the  chamber,  represented  by  the  black  portion,  the 
density  of  the  powder  will  be  its  weight  divided  by  the  weight  of 
water  that  will  fill  this  black  portion.     As  the  weight  of  water 
that  will  fill  each  volume  is  equal  to  the  volume  in  cubic  inches 
divided  by  27.68,  we  have : 

*  T     A-  27.68d) 

Density  of  Loading,    J  =  — ; — j— r — r— 

vol.  of  chamber 

27.68a 

Gravimetric  Density,  r  =  — ; — f—r 

vol.  of  charge 

27.68o) 
Density,  a=- 


vol.  of  solid  powder 
Using  metric  units  the  factor  27.68  will  be  omitted. 


INTERIOR  BALLISTICS.  55 

28.  Reduced  Length  of  Powder  Chamber.—  For  convenience  in 
the  mathematical  deductions  the  volume  of  the  powder  chamber 
is  reduced  to  an  equal  volume  whose  cross  section  is  the  same  as 
the  cross  section  of  the  bore.     The  length  of  this  volume  is  called 
the  reduced  length  of  the  powder  chamber. 
Let  u0  be  the  reduced  length  of  the  chamber, 
a>  the  area  of  cross  section  of  the  bore, 
C  the  volume  of  the  chamber, 
d  the  diameter  of  the  bore. 

Then 

C  =  UQOJ  =  u0xd?/4 

and 

?  (26) 


Reduced  Length  of  Initial  Air  Space.  —  The  air  space  in  the 
loaded  chamber,  which  includes  all  the  space  in  the  chamber  not 
occupied  by  solid  powder,  is  also  reduced  to  a  volume  whose 
cross  section  is  that  of  the  bore.  The  length  of  this  volume  is 
called  the  reduced  length  of  the  initial  air  space, 

Let  ZQ  be  the  reduced  length  of  the  initial  air  space,  in  inches. 

Then,  since  C  is  the  volume  of  the  chamber  and  C'  the  volume 
of  the  solid  powder, 

C-C* 

20  = 


at 


Substituting  for  0  and  C"  their  values  from  equations  (22) 
and  (24) 

'1      1 


Make  a==~Jd~  (27) 


Then  20w  =  27.68a<o  (23) 


56  ORDNANCE  AND  GUXNERY. 

and  since  a>  =  rd2/4 

z0  =  35.2441ad>/d2  =  [1 .54709]a<D/d2  (29) 

the  number  in  square  brackets  being  the  logarithm  of  35.2441. 

Problems. — 1.  The  volume  of  the  chamber  of  the  3-inch  field 
rifle  is  66.5  cu.  in.  The  weight  of  the  charge  is  26  oz.  Density 
of  the  powder  1.56.  What  is  the  density  of  loading,  and  what  is 
the  reduced  length  of  the  initial  air  space? 

Ans.  J=  0.6764, 

Zo  =  5.33  inches. 

2.  If  the  gravimetric  density  of  the  powder  in  the  last  example 
is  unity,  how  many  pounds  will  the  chamber  hold? 

2.4  Ibs. 

3.  The  reduced  length  of  the  initial  air  space  in  the  8-inch 
rifle  loaded  with  80  Ibs.  of  powder,  density  1.56,  is  43.72  inches. 
What  is  the  capacity  of  the  chamber? 

C  =  3617  cu.  in. 

4.  The  5-inch  siege  gun  has  a  chamber  capacity  of  402.5  cu. 
in.     What  is  the  density  of  loading  with  a  charge  of  5.37  Ibs.? 

A  =  0.3693. 

5.  The  4-inch  rifle  when  loaded  with  12  Ibs.  of  sphero-hex- 
agonal  powder  has  a  density  of  loading  of  0.915.     What  is  the 
chamber  capacity? 

C  =  363  cu.  in. 

6.  The  12-inch  rifle  has  a  chamber  capacity  of  17487  cu.  in. 
The  density  of  loading  is  0.5936.     What  is  the  weight  of  the 
charge,  and  what  is  the  volume  of  the  solid  powder  in  the  charge? 

a=i.56. 

d>  =  3751bs. 
Solid  volume  =  6654  cu.  in. 

7.  What  is  the  reduced  length  of  the  initial  air  space  in  the 
last  example? 

2o  =  95.79  inches. 


INTERIOR  BALLISTICS.  57 

8.  The  chamber  capacity  of  the  6-inch  rifle  is  2114  cu.  in. 
What  is  the  reduced  length  of  the  chamber? 

WQ  =  74.77  inches. 


PROPERTIES  OF  PERFECT  GASES. 

29.  Mariotte's  Law. — At  constant  temperature  the  tension,  or 
pressure,  of  a  gas  is  inversely  as  the  volume  it  occupies. 

As  the  density  of  a  gas  is  inversely  as  its  volume,  this  law  may 
also  be  expressed:  At  constant  temperature  the  pressure  of  a  gas 
is  proportional  to  its  density. 

Let  v  be  the  volume  of  a  given  mass  of  gas, 
p  its  pressure  in  pounds  per  unit  of  area. 

Then  if  the  volume  occupied  by  the  gas  be  changed  to  v0,  the 
temperature  of  the  gas  being  kept  constant,  the  pressure  will 
change  according  to  the  law 

vp  =  constant 

Let  PQ  represent  the  normal  atmospheric  pressure,  barometer 

30  inches; 
p0  =  14.6967  pounds  per  square  inch, 

or  103.33  kilograms  per  square  decimeter; 
VQ  the  volume  of  unit  weight  of  a  gas  at  0°  C.  under  normal 

atmospheric  pressure. 
Then  by  Mariotte's  law,  at  0°  C., 

vp  =  v0p0  (30) 

Specific  Volume. — The  specific  volume  of  a  gas  is  the  volume 
of  unit  weight  of  the  gas  at  zero  temperature  and  under  normal 
atmospheric  pressure.  VQ  in  the  above  equation  is  the  specific 
volume  of  the  gas. 

In  English  units  the  specific  volume  of  a  gas  is  the  number  of 


58  ORDNANCE  AND  GUNNERY. 

cubic  feet  occupied  by  a  pound  of  the  gas  under  the  above  condi- 
tions. 

Specific  Weight. — The  specific  weight  of  a  gas  is  the  weight  of 
a  unit  volume  of  the  gas  at  zero  temperature  and  under  normal 
atmospheric  pressure.  It  is  the  reciprocal  of  the  specific  volume. 

Gay-Lussac's  Law. — The  coefficient  of  expansion  of  a  gas  is 
the  same  for  all  gases;  and  is  sensibly  constant  for  all  tempera- 
tures and  pressures. 

Let  v0  be  the  specific  volume  of  a  gas,  vt  its  volume  at  any 
temperature  t,  and  a  the  coefficient  of  expansion.  Then  the 
variation  of  volume  under  constant  pressure  by  Gay-Lussac's  law 
will  be  expressed  by  the  equation 


or  vt 

The  value  of  a  is  approximately  1/273  of  the  specific  volume 
for  each  degree  centigrade.  The  above  equation  may  therefore  be 
written 

(31) 


30.  Characteristic  Equation  of  the  Gaseous  State.  —  The  last 
equation,  which  expresses  Gay-Lussac's  law,  may  be  combined 
with  Mariotte's  law,  introducing  the  pressure  p. 

Let  x  be  the  volume  that  vt  would  become  at  0°  C.,  under  the 
pressure  pt.  Then  by  Gay-Lussac's  law 


but  by  Mariotte's  law 

Ptx 

whence,  eliminating  x, 

Ptvt  =  Povod  +  at)  =        (273  +  0 


INTERIOR  BALLISTICS.  59 

Since  po^o/273  is  constant  for  any  gas,  put 

R  =  p0v0/273  (32) 

whence,  dropping  the  subscripts  as  no  longer  necessary, 


The  temperature  (273  +  0  is  called  the  absolute  temperature 
of  the  gas.  It  is  the  temperature  reckoned  from  a  zero  placed  273 
degrees  below  the  zero  of  the  centigrade  scale.  Calling  the  abso- 
lute temperature  T  there  results  finally 

pv  =  RT  (33) 

which  is  called  the  characteristic  equation  of  the  gaseous  state,  and  is 
simply  another  expression  of  Mariotte's  law  in  which  the  tem- 
perature of  the  gas  is  introduced. 

Equation  (33)  expresses  the  relation  that  always  exists  between 
the  pressure,  volume,  and  absolute  temperature  of  a  unit  weight 
of  gas.  To  apply  it  to  any  gas,  substitute  for  VQ  in  the  value  of 
R,  equation  (32),  the  specific  volume  of  the  particular  gas. 

For  any  number  w  units  of  weight  occupying  the  same  volume 
the  relation  evidently  becomes 

pv=wRT  (34) 

A  gas  supposed  to  obey  exactly  the  law  expressed  in  equation 
(33)  is  called  a  perfect  gas,  or  is  said  to  be  theoretically  in  the  per- 
fectly gaseous  state.  This  perfect  condition  represents  an  ideal 
state  toward  which  gases  approach  more  nearly  as  their  state  of 
rarefaction  increases. 

For  a  temperature  T'  equation  (34)  becomes 


60  ORDNANCE   AND  GUNNERY. 

Dividing  equation  (34)  by  this  equation  we  obtain 

v      T 


from  which  we  readily  see  that  if  the  pressure  of  any  mass  of  gas 
is  constant  the  volume  of  the  gas  will  vary  with  the  absolute  tem- 
perature, and  if  the  volume  is  constant  the  pressure  will  vary  with 
the  absolute  temperature. 

Problems.  —  Equations  (30)  to  (34)  are  used  in  solving  the 
following  problems. 

Specific  volumes:  Air  ................  v0=  12.391  cu.  ft. 

Hydrogen  .........  v0  =  178.891  cu.  ft. 

Coal  gas  ..........  VQ  =  24.6      cu.  ft. 

Water  gas  .........  v0  =  18.09    cu.  ft. 

1.  A  volume  of  3  cubic  feet  of  air,  confined  at  59°  F.  (15°  C.) 
and  30"  barometer,  is  heated  to  a  temperature  of  300°  C.  What 
pressure  does  it  exert? 

Vol.  of  1  Ib.  air  at  15°,  equation  (31),  vt  =  u0288/273. 


Equation  (34),  p  =  wRT/v  =  29.24  Ibs.  per  sq.  in. 

2.  Two  pounds  of  air  confined  in  a  volume  of  1  cubic  foot 
exerts  a  gauge  pressure  of  679.76  Ibs.  per  square  inch.     What  is 
its  temperature  by  the  centigrade  and  Fahrenheit  scales? 

The  total  pressure  p  is  the  gauge  pressure  plus  the  atmospheric 

pressure, 

p  =  679.76  +  14.70  =  694.46 

Equation  (34),        T  =  pv/wR  =  520.54 

Z  =  247°.54C.  =  477°.57F. 

3.  A  spherical  balloon  20  feet  in  diameter  is  to  be  inflated  with 
hydrogen  at  60°  F.,  barometer  30.2  inches,  so  that  gas  may  not 
be  lost  on  account  of  expansion  when  the  balloon  has  risen  until 


INTERIOR  BALLISTICS.  61 

the  barometer  is  at  19.6  inches  and  the  temperature  40°  F.     How 
many  cubic  feet  of  gas  must  be  put  in  the  balloon? 

The  gas  pressure  in  the  balloon  is  in  equilibrium  with  the  atmos- 
pheric pressure.  The  weight  of  gas  occupying  the  balloon  must 
be  such  that  at  40°  F.  the  pressure  will  be  in  equilibrium  with  a 
barometric  pressure  of  19.6  inches. 

p  =  poX  19.6/30  v  =  volume  of  balloon 

Equation  (34),        w  =  pv/RT  =  15.05  Ibs. 
Volume  of  w  at  60°  F.  and  30".2  barometer: 


.2/30 

v  =  wRT/p  =  2S27A  cubic  feet 

4.  What  is  the  lifting  power  at  70°  F.  (21°.ll  C.)  and  30  in. 
barometer  of  1000  cubic  feet  of  each  of  the  gases  whose  specific 
volumes  are  given? 


Air  

Vol.  1  lb.  at  70°. 
Equation  (31). 

13.35 

Pounds  in 
1000  cu.  ft. 

74.91 

Lifting  power 
1000  cu.  ft. 
Ibs. 

Hydrogen 

192.73 

5.19 

69.72 

Coal  gas 

26.5 

37.73 

37.18 

Water  eas. 

19.49 

51.31 

23.60 

5.  The  balloon  in  which  Wellman  intends  to  seek  the  North 
Pole  has  a  capacity  of  224,244  cubic  feet,  and  weighs  with  its  car 
and  machinery  6600  Ibs.  What  will  be  its  lifting  capacity  when 
rilled  with  hydrogen  at  10°  C.  and  30  inches  barometer? 

Ans.  9647  Ibs. 

31.  Thermal  Unit. — The  heat  required  to  raise  the  tempera- 
ture of  unit  weight  of  water  at  the  freezing  point  one  degree  of  the 
thermometer  is  called  a  thermal  unit. 

Mechanical  Equivalent  of  Heat. — The  mechanical  equivalent 
of  heat  is  the  work  equivalent  of  a  thermal  unit,  that  is  it  is  the 


62  ORDNANCE  AND  GUNNERY. 

work  that  can  be  performed  by  the  amount  of  heat  required  to 
raise  the  temperature  of  unit  weight  of  water  one  degree.  It  will 
be  designated  by  E.  The  unit  weight  of  water  being  one  pound, 
the  value  of  E  for  the  Fahrenheit  scale  is  778  foot-pounds;  and 
for  the  centigrade  scale,  1400.4  foot-pounds. 

In  metric  units  the  value  of  E  is  425  kilogr ammeters. 

Specific  Heat. — The  quantity  of  heat,  expressed  in  thermal 
units,  which  must  be  imparted  to  unit  weight  of  a  given  substance 
in  order  to  raise  its  temperature  one  degree  of  the  thermometer 
above  the  standard  temperature  is  called  the  specific  heat  of  the 
substance. 

The  specific  heat  of  a  gas  may  be  determined  in  two  ways: 
under  constant  pressure,  and  under  constant  volume. 

Suppose  heat  to  be  applied  to  a  unit  weight  of  gas  retained  in 
a  constant  volume  whose  walls  are  impermeable  to  heat.  The 
whole  effect  of  the  heat  will  be  to  raise  the  temperature  of  the 
gas.  If,  however,  the  gas  is  enclosed  in  an  elastic  envelope,  sup- 
posed to  maintain  a  constant  pressure  on  the  gas,  the  gas  will 
expand  on  the  application  of  heat,  and  part  of  the  heat  applied 
will  perform  the  work  necessary  to  expand  the  envelope.  There- 
fore to  raise  the  temperature  of  the  gas  one  degree,  a  greater 
amount  of  heat  must  be  applied  when  the  gas  is  under  constant 
pressure  than  when  under  constant  volume;  and  the  difference  of 
these  quantities,  that  is,  the  difference  between  the  specific  heat 
under  constant  pressure,  cp,  and  the  specific  heat  under  constant 
volume,  cv,  will  be  the  heat  that  perform^  the  work  of  expansion. 
The  mechanical  equivalent  of  a  heat  unit  being  represented  by  E, 
we  may  write 

Work  of  expansion  =  (cp—cv)E 

Actually,  part  of  the  work  that  we  have  included  in  the  work 
of  expansion  is  internal  work,  used  in  overcoming  the  attractions 
between  the  molecules;  but  the  quantity  of  work  so  absorbed  is 
small  and  is  omitted  in  the  discussions. 

The  work  of  expansion  is  equal  to  the  constant  resistance  mul- 
tiplied by  the  path.  We  will  assume  the  constant  resistance  to 


INTERIOR  BALLISTICS.  63 

be  the  atmospheric  pressure,  p0.  The  path  is  measured  by  the 
increase  of  volume  of  the  gas.  To  determine  the  path  we  have 
from  Gay-Lussac's  law,  for  the  centigrade  scale  equation  (31), 

vt-v0  =  tv0/273 

and  therefore  for  an  increase  of  temperature  of  one  degree  there 
is  an  increase  of  volume  equal  to  v0/273.  The  work  of  expansion 
for  one  degree  is  therefore  p0v0/273.  Referring  to  equation  (32), 

p0v0/273  =  R 

The  quantity  R  is  therefore  the  external  work  of  expansion 
performed  under  atmospheric  pressure  by  unit  weight  of  gas  when 
its  temperature  is  raised  one  degree  centigrade.  But  this  work  of 
expansion  has  been  found  above  to  be  equal  to  (cp—cv}E.  There- 
fore we  may  write 

(cp-  cJE  =  R  =  p0v0/273  (36) 

From  the  definition  of  specific  heat  we  deduce  that  the  quan- 
tity of  heat  necessary  to  raise  the  temperature  of  unit  weight  of 
gas  any  number  of  degrees,  as  t,  will  be 

Q=ct  (37) 

c  representing  either  cp  or  cv. 

Ratio  of  Specific  Heats. — In  the  study  of  interior  ballistics  the 
particular  values  of  cp  and  cv  for  the  different  gases  which  are 
formed  by  the  explosion  of  gunpowder  are  of  little  importance. 
It  suffices  to  know  their  ratio,  which  is  constant  for  perfect  gases 
and  approximately  so  for  all  gases  at  the  high  temperature  of 
combustion  of  gunpowder. 

The  ratio  of  the  specific  heats,  cp/cv,  is  subsequently  designated 
by  n. 

32.  Relations  between  Heat  and  Work  in  the  Expansion  of 
Gases. — The  relation  which  exists  between  the  heat  in  a  unit 


64  ORDNANCE  AND  GUNNERY. 

weight  of  gas  and  the  work  performed  in  the  expansion  of  the  gas 
may  now  be  determined  from  equation  (33), 


which  cor  tains  the  three  variables  p,  v  and  T.  If  we  suppose  an 
element  of  heat,  dq,  to  be  applied  to  the  gas,  the  effect  will  be 
generally  an  increase  in  the  temperature,  accompanied  by  an  in- 
crease in  the  pressure,  or  in  the  volume,  or  in  both  the  pressure 
and  the  volume. 

Considering  p  constant,  and  differentiating,  we  get 

dT  =  pdv/R 

and  the  quantity  of  heat  communicated  to  the  gas  will  be,  equa- 
tion (37), 

dq  = 


Considering  v  constant  we  obtain  similarly 

dq  =  cvvdp/R 

If  p  and  v  both  vary,  we  obtain  from  the  sum  of  the  partial 
differentials,  still  representing  by  dq  the  element  of  heat  applied 
to  the  gas, 

dq  =  n(cppdv  +  cvvdp)  (38) 

The  differential  of  equation  (33)  is 

RdT  =  pdv+vdp  (380 

Eliminating  vdp  between  the  last  two  equations  we  have 

pdv  (39) 


INTERIOR  BALLISTICS.  65 

The  quantity  pdv  represents  the  elementary  work  of  the  elastic 
force  of  the  gas,  while  its  volume  increases  by  dv.  The  integral  of 
pdv  is  therefore  the  total  external  work  between  the  limits  con- 
sidered. 

Representing  by  W  the  total  external  work  we  have 


=  fpdv 


(40) 


Represent  by  TI  and  T  the  initial  and  final  temperatures. 
Integrating  equation   (39)  between  the  limits  T  and  TI  we 
obtain,  since  ce,  cp,  and  R  are  constant  for  the  same  gas, 


(41) 


Isothermal  Expansion.  —  If  we  suppose  the  initial  temperature 
TI  to  remain  constant,  that  is,  that  just  sufficient  heat  is  imparted 
to  the  gas  while  it  expands  to  maintain  its  initial  temperature, 
the  quantity  T—Ti  in  equation  (41)  becomes  0,  and  solving  with 
respect  to  W  we  obtain 

R 


We  see  that  in  this  case,  since  R,  cp,  and  cv  are  constant  for  the 
same  gas,  the  external  work  done  is  proportional  to  the  quantity 
of  heat  absorbed  by  the  gas. 

Making  q  equal  to  one  thermal  unit,  W  becomes  E,  and  we 
obtain,  as  before  in  equation  (36), 


33.  Adiabatic  Expansion.  —  If  a  gas  expands  and  performs 
work  in  such  a  manner  that  it  neither  receives  heat  from  any 
extraneous  body  nor  gives  out  heat  to  an  extraneous  body,  the 


66  ORDNANCE  AND  GUNNERY. 

transformation  is  said  to  be  adiabatic.  In  this  case  part  of  the 
heat  in  the  gas  is  converted  into  work,  the  temperature  and  pressure 
of  the  gas  both  diminish,  and  the  work  performed  will  be  less  than 
for  an  isothermal  expansion. 

Since  no  heat  is  gained  or  lost,  q  becomes  0  in  equation  (41) 
and  we  have 


Make  cp/cv  =  n 

Then  W-^-^-T)  (42) 

This  equation  gives  the  value^  of  the  external  work  done  by  a 
unit  weight  of  gas  whose  temperature  is  reduced  from  TI  to  T  in 
an  adiabatic  expansion.  It  will  be  seen  that  the  external  work 
done  is  proportional  to  the  fall  of  temperature. 

LAW  CONNECTING  THE  VOLUME  AND  PRESSURE.  —  In  the  adia- 
batic expansion,  as  no  heat  is  received  from  an  external  source, 
dq  in  equation  (38)  becomes  0,  and  we  have 

Q  =  cppdv+c,vdp 

Dividing  through  by  cvpv  we  find,  since  cp/c9=n 

dv    dp 
n-  +  —  =0, 
v      p 

and  integrating,         n  loge  v  +  log*  p  =  log*  c 
whence  vnp  =  constant  =  v\np\ 

or  P" 

This  equation  expresses  the  relation  between  the  volumes  and 
pressures  of  a  gas  in  an  adiabatic  expansion. 


INTERIOR  BALLISTICS. 


67 


NOBLE   AND   ABEL'S   EXPERIMENTS. 

34.  In  1874  and  again  in  1880  Captain  Noble  of  the  English  Army 
and  Sir  Frederick  Abel  published  the  results  of  their  experiments 
on  the  explosion  of  gunpowder  in  closed  vessels.  The  purpose  of 
their  experiments  was  to  determine  definitely  the  nature  of  the 
products  of  combustion,  the  volume  and  temperature  of  the  gases, 
and  the  pressures  with  different  densities  of  loading. 

Apparatus. — The  steel  vessel  in  which  the  powder  was  ex- 
ploded was  of  great  strength  and  capable  of  resisting  very  high 
pressures. 

The  charge  of  powder  was  introduced  through  the  opening  a 
which  was  then  closed  with  a  taper  screw-plug.  A  pressure  gauge 


d  was  inserted  in  the  plug  c  and  an  outlet  was  provided  at  e  through 
which  the  gas  could  be  drawn  off  if  desired.  The  charge  was  fired 
by  electricity. 

The  vessels  were  of  two  sizes.  In  the  larger  one  a  charge  of 
2.2  pounds  of  powder  was  fired,  and  the  gases  wholly  retained. 
Black  powder  was  used  in  the  experiments. 

The  gravimetric  density  of  the  powder  used  was  unity,  so  that 


68  ORDNANCE  AND  GUNNERY. 

when  the  chamber  was  completely  filled  the  density  of  loading 
was  also  unity. 

Results  of  the  Experiments.  —  Character  of  the  Products.  —  The 
products  of  combustion  were  found  to  consist  of  about  43  per  cent 
by  weight  of  permanent  gases,  and  about  57  per  cent  of  non-gaseous 
products.  The  non-gaseous  products  ultimately  assume  the  solid 
form,  but  are  liquid  at  the  moment  of  the  explosion.  This  was 
determined  by  tilting  the  vessel  at  an  angle  of  45  degrees,  one 
minute  after  the  explosion.  Forty  five  seconds  later  it  was  re- 
turned to  its  original  position.  On  opening  the  vessel  the  solid 
residue  was  found  inclined  to  the  walls  at  the  angle  of  45  degrees. 

The  permanent  gases  are  principally  C02,  N,  and  CO,  and  the 
solids  K2CO^,  KzS,  K2S04,  and  S.  With  the  exception  of  the 
KoS  and  the  free  sulphur,  the  products  agree  in  character  with 
those  expressed  in  the  formula  generally  adopted  as  approximately 
representing  the  reaction  of  black  powder  on  explosion. 


The  formula,  however,  gives  35|  per  cent  by  weight  of  per- 
manent gases  and  64£  per  cent  of  solids. 

It  was  found,  as  was  to  be  expected,  that  in  a  closed  vessel 
variations  in  the  size,  form,  or  density  of  the  grains  had  practically 
no  effect  on  the  composition  of  the  products  of  combustion,  or  on 
the  pressures. 

Volume  of  Gases.  —  Noble  and  Abel  found  that  the  gases,  when 
brought  to  a  temperature  of  0°  C.  and  under  atmospheric  pressure, 
occupied  a  volume  of  about  280  times  the  volume  of  the  unex- 
ploded  powder. 

Specific  Volume  of  Gunpowder  Gases.  —  To  simplify  somewhat 
the  discussions  concerning  the  gases  of  fired  gunpowder  we  will  use 
as  the  specific  volume  the  volume,  at  0°  C.  and  under  atmospheric 
pressure,  of  the  gases  produced  by  the  combustion  of  unit  weight 
of  powder.  That  is,  we  will  consider  this  weight  of  gas  as  unit 
weight. 


INTERIOR  BALLISTICS.  69 

35.  Relation  between  Pressure  and  Density  of  Loading.— 

The  relation  between  the  pressure,  volume,  and  absolute  tem- 
perature of  the  gases  from  a>  units  of  weight  of  powder  at  the 
moment  of  explosion  is  given  by  equation  (34). 


Make  f  =  RT  (44) 

and  we  obtain  from  (34),  for  the  pressure  exerted  by  the  gases  from 
&  pounds  of  powder,  the  gases  occupying  the  volume  v  at  the 
temperature  of  explosion, 

p  =  f(D/v  (45) 

FORCE  OF  THE  POWDER.  —  If  we  make  both  a>  and  v  unity  in  this 
equation,  p  becomes  equal  to  /.  /  is  therefore  the  pressure  per 
unit  of  surface  exerted  by  the  gases  from  unit  weight  of  powder, 
the  gases  occupying  unit  volume  at  the  temperature  of  explosion. 
/  is  called  the  force  of  the  powder. 

Let  a  be  the  volume  of  the  residue  from  unit  weight  of  powder, 

C  the  volume  of  the  chamber. 

Then  the  volume  occupied  by  the  gas  from  d>  units  of  powder  will 
be 

v  =  C—  a<i) 

We  may  introduce  the  density  of  loading,  using  metric  units 
by  substituting  for  C  in  this  equation  its  value  &/A  from  equation 
(23),  and  obtain 

»-£(l-aJ) 

Substituting  this  value  of  v  in  (45)  we  obtain 


(46) 


This  equation  expresses  the  relation  between  the  pressure  of  the 
gases  from  &  units  of  weight  of  powder  and  the  density  of  loading. 


70  ORDNANCE  AND   GUNNERY. 

J  1 

When  .  -  -  =  1,  that  is,  when  J  =  -r—  -  (460 

1  —  OLa  \.-\-(X. 


Comparing  the  value  of  J  in  equation  (46')  with  the  general 
value,  J  =  <D/C,  we  see  that  in  (46')  the  weight  of  powder  is  unity, 
and  the  volume  of  the  chamber  l  +  «.  The  volume  occupied  by 
the  gas  is  therefore  also  unity.  The  pressure  therefore  becomes 
in  this  case  the  force  of  the  powder  as  defined  above. 

By  substituting  in  equation  (46)  two  observed  values  of  p  cor- 
responding to  different  values  of  J,  the  values  of  a  and  /  were 
determined.     As   the   means   of   many   observations   Noble   and 
Abel  finally  adopted  the  values: 
a  =  0.57; 

/  =  18.49  tons  per  square  inch 
=  291200  kilograms  per  square  decimeter 
The  pressure  for  any  density  of  loading  is  given  by  the  equation 

j 

ft  =  18.49::  —  ~  „  .  tons  per  square  inch 
1  —  0.5/J 

When  J  =  l  the  equation  gives  p  =  43  tons  per  square  inch. 

The  value  of  a,  0.57,  means  that.  the  volume  occupied  at  the 
temperature  of  explosion  by  the  liquid  residue  from  one  kilogram 
of  powder  is  57/100  of  one  cubic  decimeter.  With  gravimetric 
density  unity  one  kilogram  of  powder  occupies  one  cubic  decimeter. 
Referring  now  to  equation  (21),  we  sec  that  the  solid  powder,  of 
ordinary  density  and  of  gravimetric  density  unity,  occupies  57/100 
of  the  volume  of  the  charge  in  granular  form.  The  volume  of  the 
residue  at  the  temperature  of  explosion  is  therefore  practically 
equal  to  the  volume  of  the  solid  powder  in  the  charge. 

36.  Temperature  of  Explosion.  —  The  temperature  of  explosion 
may  now  be  determined  from  equation  (44),  which  with  (32)  gives 


(47) 


INTERIOR  BALLISTICS.  71 

VQ  is  the  volume  occupied  by  the  gas  from  unit  weight  of  pow- 
der. Since  the  volume  of  this  quantity  of  gas  is  280  times  the 
volume  of  the  powder,  and  one  kilogram  of  powder  occupies  one 
cubic  decimeter,  v0  =  280  cubic  decimeters.  p0,  the  atmospheric 
pressure,  is  103.33  kilograms  per  square  decimeter.  Substituting 
these  with  the  value  of  /,  291200  kilograms  per  square  decimeter, 
we  find  T  =  2748°  C.  As  this  is  the  absolute  temperature,  subtract- 
ing 273  we  find  the  temperature  of  explosion  to  be  2475°  C. 

Captain  Noble  later  considered  the  absolute  temperature  as 
2505°  C. 

The  approximate  correctness  of  these  temperatures  was  verified 
by  the  introduction  of  pieces  of  fine  platinum  wire  into  the  explo- 
sion chamber.  The  platinum,  which  melts  at  about  2000°  C., 
was  partially  fused. 

Mean  Specific  Heat  of  Products.  —  The  quantity  of  heat  given 
off  by  one  kilogram  of  powder  was  found  to  be  705  calories,  that 
is,  the  heat  necessary  to  raise  705  kilograms  of  water  one  degree 
centigrade.  From  the  relation  Q  =  ct,  equation  (37),  t  being  the 
actual  temperature  of  explosion,  not  the  absolute,  a  value  was 
found  for  the  mean  specific  heat  of  the  products: 

705 


Relations  between  Volume   and   Pressure   in   the   Gun.  — 

Noble  and  Abel  found,  contrary  to  their  expectations,  that  the 
pressures  in  closed  vessels  did  not  differ  greatly  from  the  pres- 
sures hi  guns  when  the  powder  in  the  gun  was  wholly  consumed 
or  nearly  so.  They  concluded  from  this  that  the  expansion  of 
the  gases  in  the  gun  did  not  take  place  without  the  addition  of 
heat;  but  that  the  gases  received  during  the  expansion  the  heat 
stored  in  the  finely  divided  liquid  residue. 

Let  Ci  be  the  specific  heat  of  the  residue,  assumed  to  be  con- 
stant. The  elementary  quantity  of  heat  given  up  by  each  unit 
weight  of  residue  will  then  be  CidT.  If  there  are  Wi  units  of  weight 


72  ORDNANCE  AND  GUNNERY. 

of  residue,  w\c\dT  units  of  heat  will  be  yielded  to  the  gases;  and 
if  there  are  102  units  of  weight  of  gas,  each  unit  will  receive,  in  heat 
units, 


/?  being  the  ratio  w:/W2,  and  the  negative  sign  being  used  be- 
cause T  decreases  while  q  increases. 

Substituting  this  value  of  dq  in  equation  (39)  it  becomes 


Eliminate  RdT  by  means  of  (38');   divide  through  by  pv,  and 
integrate,  considering  CP,  cv,  c\  and  /?  constant.     We  will  obtain 


,+Cp 


p-JH7r  (48) 

When  there  is  no  residue  /?  is  0,  and  the  equation  becomes 
identical  with  equation  (43),  which  was  deduced  for  an  adiabatic 
expansion.  In  both  these  equations  v\  and  v  are  the  volumes 
actually  occupied  by  the  gases,  exclusive  of  the  residue. 

Assume  the  gravimetric  density  and  density  of  loading  to  be 
unity,  that  is,  the  chamber  is  filled  with  powder,  and  that  the 
powder  is  all  burned  before  the  projectile  moves.  Then  v\  in 
equation  (48)  will  be  the  volume  occupied  by  the  gases  in  the 
chamber  of  the  gun,  and  pi  the  corresponding  pressure.  If  we 
call  i/  the  volume  of  the  chamber,  avr  will  be  the  volume  of  the 
residue,  and  if  —  av'  =  v\  the  volume  of  the  gases;  and  if  we  call 
v"  the  volume  behind  the  projectile  at  any  instant,  the  volume 
v  occupied  by  the  gases  becomes  v"  —  av'  =  v.  Equation  (48) 
therefore  becomes 

P-fr&r—^}****  (48') 

r      ^i\i}"  —  av    I 


INTERIOR  BALLISTICS.  73 

These  values  for  the  constants  were  determined  in  the  experi- 

ments. 

pi  =  13  tons  per  square  inch 

a  =  0.57  v'  =  27.68o) 

/2  =  1.2957        cp=0.2324 
d  =  0.45  c,  =  0.1762 

From  these  values  we  find  the  ratio  of  the  specific  heats, 
cp/c,,  =  n  =  1.32.  The  value  of  the  exponent  in  (48')  is  1.074. 

37.  Theoretical  Work  of  Gunpowder.  —  The  general  expression 
for  the  work  done  by  a  gas  expanding  from  a  volume  Vi  to  a  vol- 
ume v  is 

W=  (*  pdv 

JVl 

Substituting  for  p  its  value  from  (43)  and  integrating, 


Assuming  that  the  powder  is  all  burned  before  the  projectile 
moves,  and  that  the  gravimetric  density  and  density  of  loading 
are  unity,  the  values  Vi  and  v  in  this  equation  may  be  replaced 
as  indicated  in  equation  (480,  and  we  obtain 


i- 


_  /i/(l-a)\*-i  ) 
\*'-cnf  )       ) 


This  is  the  expression  for  work  under  the  adiabatic  expansion 
for  which  n  =  1.32.  If  we  substitute  for  n  the  value  1.074,  which  is 
the  value  of  the  exponent  in  equation  (480,  the  equation  will  then 
apply  to  Noble  and  Abel's  hypothesis. 

Work  at  Infinite  Expansion. — When  the  length  of  the  bore  is 
infinite,  v"}  which  is  the  volume  behind  the  projectile,  is  infinite, 
and  we  have 

pli/(l-«) 
n-1 


74  ORDNANCE  AND  GUNNERY. 

To  obtain  the  work  of  the  gases  from  one  pound  of  powder 
make  v'  =  27.68  cubic  inches,  the  volume  occupied  by  one  pound, 
the  gravimetric  density  being  unity.  Make  n  =  1.32,  and  substi- 
tute for  the  other  constants  the  values  given  on  page  73.  Divide 
by  12  to  reduce  from  inch-tons  to  foot-tons. 

We  find  for  the  work  of  one  pound  of  powder  expanding  adi- 
abatically  to  infinity 

W  =  133.3  foot-tons  per  pound. 

Substituting  for  n  the  value  of  the  exponent  in  equation  (48'), 
1.074,  we  obtain,  under  Noble  and  Abel's  hypothesis  that  the  gases 
received  heat  from  the  residue, 

W  =  576.35  foot-tons  per  pound. 


FORMULAS   FOR   VELOCITIES   AND  PRESSURES    IN 

THE   GUN. 

38.  Elements  Considered.  Assumptions. — Formulas  connect- 
ing the  velocity  of  the  projectile  with  its  travel  in  the  bore  may 
be  deduced  from  the  relations  we  have  established  involving  the 
work  of  the  powder;  but  these  formulas,  while  they  include  the 
force  of  the  powder,  do  not  include  consideration  of  the  individual 
characteristics  of  different  powders,  such  as  form  and  size  of  grain, 
density,  and  velocity  of  combustion  in  the  air;  nor  consideration 
of  the  effect  on  the  combustion  of  the  variable  pressure  in  the  gun. 

M.  Emile  Sarrau,  engineer-in-chief  of  the  French  powder  fac- 
tories, was  the  first  to  include  these  elements  in  ballistic  formulas. 
He  considers  the  progressive  combustion  of  the  charge  under  the 
influence  of  the  varying  pressure  in  the  gun,  regarding  the  powder 
as  a  variable  in  the  formulas.  The  individual  characteristics  of 
the  powder  employed  enter  the  formulas,  which  thereby  become 
applicable  to  the  determination,  in.  advance,  of  the  proper  weight 
of  charge,  the  kind  of  powder,  the  best  form  and  size. of  grain  to 
produce  desired  results  in  a  given  gun. 


INTERIOR  BALLISTICS.  75 

Sarrau  assumes  that  the  time  required  for  complete  inflam- 
mation of  the  charge  is  negligible  compared  with  the  time  of 
combustion.  He  also  assumes  an  adiabatic  expansion  of  the 
gases. 

This  latter  assumption,  while  incorrect  according  to  the  ex- 
periments of  Noble  and  Abel,  is  now  generally  made  by  writers 
on  interior  ballistics;  and  whatever  error  is  introduced  through 
the  assumption  is  later  corrected  in  the  determination,  by  experi- 
ment, of  the  constants  in  the  formulas. 

Principle  of  the  Covolume.  —  Another  assumption  of  important 
bearing  in  the  deduction  of  the  ballistic  formulas  will  now  be 
explained. 

The  characteristic  equation  for  perfect  gases,  equation  (33), 
combined  with  equation  (47)  gives  for  the  pressure  from  unit 
weight  of  gas  confined  in  the  volume  v, 

p  =  f/v 

But  it  has  been  found  by  experiment  that  for  the  gases  of 
explosion  the  law  expressed  by  this  equation  does  not  hold,  and 
that  to  obtain  the  true  value  of  the  pressure  we  must  diminish  the 
volume  v,  which  is  the  volume  of  the  explosion  chamber.  The 
true  equation  must  therefore  be  of  the  form 

(49) 


v-a 


We  may  call  the  volume  v—  a  the  effective  volume  of  the  gas. 

Theoretical  deductions  indicate  that  the  subtractive  volume  a 
is  the  actual  volume  of  the  incompressible  molecules  in  a  unit 
weight  of  powder  gas;  that  is,  it  is  the  limiting  volume  beyond 
which  a  unit  weight  of  gas  cannot  be  compressed. 

The  volume  a  is  called  the  cowlume.  Sarrau  determined 
by  experiment  with  different  gases  that  the  mean  value  of 
the  covoiume  is  one  one-thousandth  of  the  specific  volume  of 
the  gas.  Other  writers  take,  for  convenience,  the  reciprocal 


76  ORDNANCE  AND  GUNNERY. 

of  the  density  of  the  powder  as  the  covolume,  this  value 
not  differing  greatly  from  the  other.  We  have  seen,  equation 
(20),  that  when  the  gravimetric  density  is  unity  the  volume  of  the 
solid  powder  in  unit  volume  of  the  charge  is  the  reciprocal  of 
the  density  of  the  powder.  The  assumption  of  the  reciprocal  of 
the  density  as  the  covolume  is  equivalent  therefore  to  considering 
the  covolume  as  the  volume  originally  occupied  by  unit  weight 
of  solid  powder. 

Under  this  assumption  the  volume  v— a,  equation  (49),  which 
is  the  effective  volume  of  unit  weight  of  the  powder  gases,  becomes 
the  volume  of  the  powder  chamber  minus  the  volume  of  the  solid 
powder  in  unit  weight  of  the  charge. 

The  effective  volume  of  the  gases  from  the  whole  charge  will 
therefore  be  the  volume  of  the  powder  chamber  minus  the  volume 
of  the  solid  powder  in  the  whole  charge. 

But  this  is  the  initial  air  space  in  the  chamber.  Therefore 
the  effective  volume  occupied  by  the  powder  gases  in  the  chamber  is 
the  initial  air  space. 

If  the  powder  leaves  a  non-volatile  residue,  the  volume  of  this 
residue  at  the  temperature  of  explosion  must  be  added  to  the 
covolume  of  the  gases  formed,  a  in  equation  (49)  will  then 
represent  the  covolume  of  the  gases  from  unit  weight  of  powder 
plus  the  volume  of  the  residue  from  unit  weight  of  powder. 

39.  Differential  Equation  of  the  Motion  of  a  Projectile  in  a 
Gun. — Let 

y  be  the  weight  of  powder  burned  at  the  time  t, 
T\  the  absolute  temperature  of  combustion, 
T  the  absolute  temperature  of  the  gas  at  the  time  t. 

The  work  of  a  unit  weight  of  gas  in  an  adiabatic  expansion 
between  the  temperatures  T\  and  T  is  given  by  equation  (42). 
For  a  weight  of  gas  y  we  have 


INTERIOR  BALLISTICS.  77 

From  equation  (44),  since  T\  now  represents  the  temperature 
of  explosion,  the  value  for  the  force  of  the  powder  is  f  =  RTi; 
and  from  equation  (34),  pv  =  yRT.  With  these  substitutions  the 
above  equation  becomes 

(n-l)W  =  fy-pv  (50) 

In  this  equation  v  is  the  volume  occupied  by  the  gases  at  the 
temperature  T  and  at  the  time  t. 

Let  u  be  the  distance  traveled  by  the  projectile  at  the  time  t, 
to  the  cross  section  of  the  bore, 
ZQ  the  reduced  length  of  the  initial  air  space. 

Under  the  assumption  of  the  volume  originally  occupied  by 
unit  weight  of  solid  powder  as  the  covolume  of  the  gases,  the 
initial  air  space  in  the  chamber  becomes  the  volume  occupied  by 
the  powder  gases  in  the  chamber. 

We  therefore  have,  for  the  volume  occupied  by  the  gases  at 
the  time  t, 


Substituting  this  value  in  equation  (50)  we  have 

(51) 


an  equation  expressing  the  relation  at  each  instant  between  the 
weight  of  powder  burned,  the  pressure,  the  travel  of  the  projectile, 
and  the  external  work  performed. 

In  introducing  the  velocity  of  the  projectile  we  will  assume  that 
the  whole  work  of  the  gas  is  expended  in  giving  motion  of  transla- 
tion to  the  projectile.  Making  w  the  weight  of  the  projectile, 
and  representing  now  by  v  the  velocity  of  the  projectile, 


2g        2g\dt 
p  in  (51)  is  the  pressure  per  unit  of  area;   top  the  total  pressure 


78  ORDNANCE  AND   GUNNERY. 

on  the  base  of  the  projectile.  The  acceleration  of  the  projectile  is 
d?u/dt2.  The  total  pressure  on  the  base  of  the  projectile  is  equal 
to  the  product  of  the  mass  by  the  acceleration.  Therefore 

w  d?u 


Substituting  these  values  of  W  and  ajp  in  (51)  we  have 

.d?u     n—l/du\2     f  v 


(53> 

which  is  Sarrau's  differential  equation  of  the  motion  of  a  projectile 
in  the  bore  of  a  gun. 

In  deducing  this  equation  there  were  neglected  the  following 
energies. 

The  heat  communicated  by  the  gases  to  the  walls  of  the  gun, 

The  work  expended  on  the  charge,  on  the  gun,  and  in  giving 
rotation  to  the  projectile, 

The  work  expended  in  overcoming  passive  resistances,  such  as 
the  forcing  of  the  band,  the  friction  along  the  bore,  and  the  resist- 
ance of  the  air. 

Dissociation  of  Gases.  —  The  error  committed  by  the  omission 
of  these  energies  may  not  be  as  great  as  would  at  first  appear, 
for  we  have  also  omitted  from  consideration  the  heat  supplied  by 
the  phenomenon  called  dissociation.  According  to  Berthelot  the 
composition  of  the  complex  gases  from  fired  gunpowder  is  not 
permanent,  and  at  the  high  temperature  during  the  first  instants 
of  explosion  these  gases  decompose  into  more  simple  combinations  , 
perhaps  into  their  elements.  The  increase  in  volume  due  to  the 
displacement  of  the  projectile  causes  a  reduction  in  the  tempera- 
ture, which  permits  the  dissociated  gases  to  combine  again  with  a 
consequent  development  of  heat.  The  theory  of  dissociation 
forms  the  basis  for  the  assumption  of  some  writers  on  ballistics, 
notably  Cblonel  Mata  of  the  Spanish  artillery,  that  by  reason  of 
this  phenomenon  the  expansion  of  the  gases  in  the  gun  takes  place 


INTERIOR  BALLISTICS.  79 

as  though  the   gases  received  heat  from  the  exterior,  and  not 
adiabatically. 

It  will  be  seen,  however,  from  the  form  of  equation  (53)  that 
the  errors  of  assumption  may  be  allowed  for  by  giving  to  /  a  suit- 
able value,  and  this  without  changing  the  form  of  the  differential 
equation  of  motion.  The  force  of  the  powder  as  it  appears  in 
equation  (53)  can  therefore  be  considered  only  as  a  coefficient 
whose  value  must  be  determined  by  experiment. 

Sarrau  deduced  from  the  differential  equation  of  motion  for- 
mulas for  the  velocity  and  pressure  as  functions  of  the  travel  of 
the  projectile. 

40.  Ingalls*  Formulas.  —  We  will  now  follow  Colonel  Ingalls, 
United  States  Army,  in  the  deduction  of  his  formulas.  These 
formulas  are  considered  as  giving  more  accurate  results  than 
Sarrau's  formulas,  for  the  velocity  and  pressures  produced  by 
modern  powders  in  the  bore  of  the  gun;  and  the  use  of  Sarrau's 
formulas  is  generally  limited  to  the  determination  of  muzzle 
velocities  and  maximum  pressures. 

Let  v  be  the  velocity  of  the  projectile  in  the  bore  at  the  time  t. 

Then 

du 

ar-f 

and 

d?u    dv    vdv 


Substituting  these  values  in  equation  (53)  it  becomes 

(55) 


The  true  value  of  n,  the  ratio  of  the  specific  heats,  cp/cv,  is  un- 
certain. For  perfect  gases  its  value  is  1.41.  Regarding  the  pow- 
der gases  at  the  high  temperature  of  explosion  as  perfect  gases, 
earlier  writers  assumed  this  value  for  n.  Recent  investigations 


80  ORDNANCE  AND  GUNNERY. 

have  shown  that  the  value  of  1.41  is  too  great.  Some  recent 
writers  adopt  the  value  unity  for  n.  As  we  have  seen,  equation 
(35),  the  work  of  expansion  is  directly  proportional  to  the  differ- 
ence of  the  specific  heats;  and  if  their  ratio  is  unity  and  the  differ- 
ence between  them  zero,  there  can  be  no  external  work  performed. 
The  assumption  of  the  value  unity  is  made  for  convenience,  and 
the  error  due  to  the  assumption  is  compensated  for,  with  the  other 
errors,  in  the  experimental  determination  of  the  values  of  the 
constants. 

Ingalls  assumes  the  value  n  =  4/3,  which  is  practically  the 
value  deduced  from  the  experiments  of  Noble  and  Abel,  see  page 
73. 

Making  n  =  4/3  in  equation  (55)  we  obtain 


(56) 

Make 

x  —  U/ZQ  (57) 

«s 

Under  the  assumption  made  that  the  covolume  of  the  gases  is 
equal  to  the  volume  occupied  by  the  solid  powder  in  the  charge, 
the  initial  air  space  is  the  volume  occupied  by  the  gases  in  the 
powder  chamber.  Considering  z0,  which  is  the  reduced  length  of 
the  initial  air  space,  as  the  measure  of  this  volume,  x  in  equation 
(57),  z  =  w/2o,  becomes  the  number  of  expansions  of  the  volume 
occupied  by  the  powder  gases  in  the  chamber,  when  the  projectile  has 
traveled  the  distance  u. 

It  is  important  to  bear  in  mind  that  x  represents  a  number  of 
expansions,  and  u  the  distance  traveled  by  the  projectile. 

Making  x  =  u/z0,  equation  (55)  becomes 


(58) 


y,  the  weight  of  powder  burned,  is  a  function  of  the  time  and 
also  of  the  travel  u,  and  of  x.    The  integration  of  this  equation 


INTERIOR  BALLISTICS.  81 

even  when  the  simplest  admissible  form  of  y  as  a  function  of  x  is 
assumed  has  not  yet  been  possible. 

Considering  y  constant  the  equation  may  be  integrated.    Re- 
arranging it. 


w 
And  integrating, 


When  z=0,  v=0,  and  C=—£fgy/w.    Therefore 

1 


(g) 


Making  i/  constant  in  equation  (58)  is  equivalent  to  assuming 
instantaneous  combustion  for  that  part  of  the  charge  that  has 
burned  at  the  time  t.  We  know  this  to  be  in  error  since  the  com- 
bustion of  the  charge  is  progressive.  If,  however,  we  determine 
the  values  of  the  constants  in  the  equations  by  substituting  meas- 
ured values  of  v,  we  obtain  an  equation  that  is  true  for  the  meas- 
ured values,  and  may  be  true  for  other  values  of  v  at  other  points 
in  the  bore.  Only  by  experiment  can  we  determine  whether  re- 
sults obtained  under  this  supposition  are  correct;  and  experiment, 
as  stated  by  Colonel  Ingalls,  is  the  final  test  of  nearly  all  physical 
formulas. 

41.  Velocities  in  the  Bore.  —  To  make  equation  (59)  applicable 
to  points  in  the  bore  we  must  determine  a  relation  between  the 
quantity  of  powder  burned  at  any  instant  and  the  corresponding 
travel  of  the  projectile,  that  is,  we  must  determine  the  value  of  y 
as  a  function  of  u  or  x.  Then  substituting  for  y  in  the  equation 
this  value,  which  for  any  powder  will  contain  x  as  the  only  varia- 
ble, we  will  have  the  desired  equation  expressing  the  relation 
between  the  velocity  of  the  projectile  and  its  travel  in  the  bore. 


82  ORDNANCE  AND  GUNNERY. 

Combustion  under  Variable  Pressure.  —  We  have  previously 
deduced,  page  26,  an  expression  for  the  quantity  of  the  powder 
burned,  under  constant  pressure,  as  a  function  of  the  thickness  of 
layer  burned.  This  relation  is  given  by  equation  (16)  on  that 
page. 

I   [          I          I2} 

y  =  war\l  +  Xr  +  fjir2\  (60) 

to  i  t0         to  j 

in  which  y  is  the  weight  of  the  powder  burned  when  a  thickness  of 
layer  I  has  been  burned,  <i>  is  the  weight  of  the  charge,  10  is  half  the 
least  dimension  of  the  powder  grain,  and  a,  A,  and  fj.  are  constants 
of  form  of  the  grain. 

Representing  by  T  the  time  of  combustion  in  air  of  the  whole 
grain,  or  charge,  the  uniform  velocity  of  combustion  will  be  I0/r. 

In  the  gun  the  powder  burns  under  variable  pressure,  and  the 
velocity  of  combustion  is  expressed  by  dl/dt.  Assuming  that  the 
velocity  of  combustion  varies  as  some  power  of  the  pressure,  and 
representing  by  p0  the  pressure  of  the  atmosphere  under  which  the 
velocity  of  combustion  is  I0/r,  we  obtain  the  equation 


= 
at 

in  which  p  represents  the  pressure  on  the  base  of  the  projectile  at 
any  instant. 

The  exponent  </>  is  given  different  values  by  different  writers. 
Sarrau  assumes  <£  =  l/2.  Recent  experiments  indicate  a  mean 
value  of  0.8.  The  value  unity  is  assumed  by  other  writers.  In- 
galls  assumes  the  value  1/2  with  Sarrau. 

The  pressure  per  unit  of  area  on  the  base  of  the  projectile  is, 
from  equation  (52), 

w 

p  = 
cog 

Substituting  this  value  of  p  in  equation  (61)  and  using  equation 


INTERIOR  BALLISTICS.  83 

(54)  and  the  relations 

dx    1  du    v 

•£*'0>      •  •      7.   =     ~  ~77~  == 

ut       ZQ  Ut       ZQ 

and 

dl_dl  dx_dl  v 
dt    dxdt 


equation  (61)  may  be  brought  to  the  form 
d,Q/  wz0 


_ 
dx     r   2gojp      \  dx  /    v 

Integrating  and  dividing  by  10, 


I0~r  \2gwpo 
Make 


11  I  wzp  \*   r/d(v2)\*l 
~  J   \  dx  )   v 


(63) 

> 

Then  1/10  =  KX0  (65) 

Substituting  this  value  in  (60)  we  have 

y  =  a>aKX0  {  1  +  XKX0  +  //(KZ0)2  }  (66) 


42.  DISCUSSION  OF  VALUES.  —  The  value  of  K  in  this  equation 
is  composed  wholly  of  constants,  a,  A,  and  fj.  are  the  constants  of 
form  of  the  powder  grain.  By  the  differentiation  of  equation 
(59)  and  substitution  in  (64),  see  foot-note,  page  84,  we  find  for 
the  value  of  X0 


(67) 


84  ORDNANCE   AND  GUNNERY. 

X0  is  therefore  a  function  of  x  only,  and  x  from  its  value,  x  =  U/ZQ, 
is  itself  a  function  of  the  travel  of  the  projectile.  Equation  (66) 
therefore  expresses,  for  powder  of  any  particular  granulation,  the 
relation  between  the  weight  burned  at  any  instant  and  the  corre- 
sponding travel  of  the  projectile. 

This  equation  may  be  put  into  another  form. 

At  the  instant  that  the  powder  is  all  burned  in  the  gun,  y  =  a 
and  I  =  IQ.  We  will  distinguish  the  particular  values  of  the  various 
quantities  at  the  instant  that  the  burning  of  the  powder  is  com- 
pleted by  putting  a  dash  over  the  symbol. 

When  y  =  at  and  /  =  IQ,  equations  (65)  and  (66)  then  become 

KX0  =  l  (68) 


This   last  relation  has  been  previously  established  in  equa- 
tion (5). 

Substituting  the  value  of  K  from  (68)  in  (66),  we  obtain 


^  =  ^-X0  i  1  +  -—  Xo  +  ^AV  j- 
<o    X0    °(       X0         AV        f 


(69) 


We  have  now,  in  X0,  introduced  into  the  value  of  y  the  travel 
of  the  projectile  at  the  specific  instant  that  the  burning  of  the 
charge  is  complete. 

(59) 


3(1  +  z) 


/dfo' 
\dx 


/* 
From  equation  (64),     X0=  I 

^ 


dx  I    v 

V       U    V        ^. 

dx 


INTERIOR  BALLISTICS.  85 

Make 

(70) 


and  Xl/X0^X2  (71) 

whence  Z«l-~  (72) 


From  equation  (59)  we  obtain  for  the  velocity  at  the  instant 
that  the  burning  of  the  charge  is  complete, 


=  69^X2  (73) 


43.  Velocity  of  the  Projectile  while  the  Powder  is  Burn- 
ing. —  Substituting  in  equation  (59)  the  value  of  Qgf  from  (73)  and 
the  value  of  y  from  (69),  using  equation  (71),  and  making 


N^  (74) 

Xl  X0  Z02 

equation  (59)  reduces  to  the  form 

v>  =  MXl  {  1  +  NX0+  N'X<?\  (75) 

This  equation  expresses  the  value  of  the  velocity  of  the  pro- 
jectile at  any  instant  while  the  powder  is  burning,  in  terms  of  the 
variable  travel  of  the  projectile,  and  of  its  velocity  and  travel  at 
the  instant  of  the  complete  burning  of  the  charge. 

Velocity  after  the  Powder  is  Burned.  —  Distinguish  with  the 
subscript  a  the  values  of  v  and  p  after  the  charge  is  completely 
burned,  y  is  then  equal  to  at,  and  equation  (59)  when  combined 
with  (73)  and  (72)  becomes 

$z  (76) 


86  ORDNANCE  AND  GUNNERY. 

and  making  Vi2  =  v2/X2  (77) 

we  have  v<2  =  V]2X2  (78) 

which  is  the  formula  for  the  velocity  after  the  powder  is  all  burned. 

This  equation  is  identical  with  equation  (59),  if  in  the  latter 
we  make  y  =  a>.  Vi2  =  6fga>/w,  see  (73)  and  (77),  and  X2  is  an 
abbreviation  for  the  quantity  in  brackets,  see  (72). 

As  explained  under  equation  (59),  equation  (78)  is  therefore 
the  equation  of  the  velocity  under  the  supposition  that  the  powder 
is  all  burned  before  the  prftjfif  f  *1ci  |yr*wg 

The  Velocity  Vi.  —  From  equation  (78)  we  see  that  V\  is  what 
i'0  becomes  when  X2  is  equal  to  unity;  and,  equation  (72),  X2  is 
unity  when  x  is  infinite.  V\  is  therefore  the  velocity  corresponding 
to  an  infinite  travel  of  the  projectile. 

44.  Relation  between  the  Velocities  Before  and  After  the 
Burning  of  the  Charge.  —  Make 

k  =  y/ti>  =  fraction  of  charge  burned. 

Replacing  M,  N,  and  N'  in  equation  (75)  by  their  values,  and 
combining  with  equations  (69),  (70),  and  (76)  we  may  establish 
the  relation 

v  =  vaVk  (79) 

That  is,  the  velocity  of  the  projectile  before  the  charge  is  con- 
sumed is  equal  to  what  the  velocity  would  have  been  at  the  same 
point  if  all  the  charge  had  been  burned  before  the  projectile  moved, 
multiplied  by  the  square  root  of  the  fraction  of  charge  burned. 

Relation  between  the  Weight  of  Powder  Burned  and  the 
Velocity  and  Travel  of  the  Projectile.  —  Replacing  va  in  equation 
(79)  by  its  value  from  (78)  we  obtain 


X2    or     y  =  u>v2/Vl2X2  (80) 

equations  that  will  be  found  convenient  for  determining  the  frac- 


INTERIOR  BALLISTICS.  87 

tion  of  charge  or  weight  of  powder  burned  when  the  velocity  and 
travel  of  the  projectile  are  known. 

By  reason  of  the  form  assumed  by  the  value  of  k  for  certain 
grains  very  simple  relations  may  be  established,  for  these  grains, 
between  the  fraction  of  charge  burned  and  the  travel  of  the  pro- 
jectile. 

CUBICAL,  SPHERICAL,  AND  SPHEROIDAL  GRAINS.  —  For  cubical 
grains  a  =  3,  A=  —  1,  and  /*  =  l/3  (see  page  20).  These  values 
apply  also  to  spherical  and  spheroidal  grains.  Substituting  them 
in  equation  (69)  we  obtain 


(81) 
and  X0  =  X0{l-(l 


From  the  first  equation  we  may  obtain  the  fraction  of  charge 
burned  for  any  travel  of  the  projectile,  and  the  converse  from  the 
second. 

SLENDER  CYLINDRICAL  AND  PRISMATIC  GRAINS.  —  For  long 
slender  cylinders 


XQ/  (82) 


which  also  apply  to  grains  in  the  form  of  long  slender  prisms  of 
square  cross  section. 

For  other  forms  of  grain  the  solution  of  a  complete  cubic  equa- 
tion is  necessary  to  determine  X0  when  k  is  known. 

45.  Pressures. — The  general  expression  for  the  pressure  per 
unit  of  area  on  the  base  of  the  projectile  is  given  in  equation  (62). 
Transforming  this  equation  by  means  of  (54)  and  (57)  we  obtain 

»  aw 

2ga)z0    ax 
By  substituting  in  succession  the  values  of  d^^/dx  obtained 


88  ORDNANCE  AND  GUNNERY. 

from  the  equations  for  velocity  before  and  after  the  complete 
burning  of  the  charge  we  will  obtain  the  values  of  p  that  apply 
before  and  after  the  charge  is  burned. 

Pressure  While  the  Powder  is  Burning.— Finding  the  value  of 
d(v2)/dx  from  equation  (75),  see  foot-note,  and  making 


X3=dX1/dx 


X3dx 


(84) 


(85) 


we  obtain  for  the  pressure  per  unit  of  area  on  the  base  of  the  pro- 
jectile while  the  powder  is  burning 

p  =  M'X3\l  +  NX4  +  NfX5]  (86) 

It  will  be  observed  that  X3,  X±,  and  X5  are  all  functions  of  x 
only.  The  logarithms  of  their  values  for  various  values  of  x  will 
be  found  in  Table  I  at  the  end  of  the  volume. 

Pressure  After  the  Powder  is  Burned.  —  Finding  the  value  of 
d(v*)/dx  from  equation  (78),  Vi2  being  constant,  we  obtain  with 
the  aid  of  (72) 

d(vt?)_Vl2dX2_     V? 
dx  dx        3(1  +  *)* 

J]  (75} 


=  *+x        +MN'  l 

dx  dx  \    °  dx         '  dx  /  \    w    dx  "  dx 

Make 


INTERIOR  BALLISTICS.  89 

Substituting  in  (83)  and  making 


we  obtain  for  the  pressure  per  unit  of  area  on  the  base  of  the  pro- 
jectile after  the  powder  is  all  burned 


(88) 


46.  Maximum  Pressure.  —  The  maximum  pressure  in  a  gun 
occurs  when  the  projectile  has  moved  but  a  short  distance  from 
its  seat,  or  when  u  and  x  are  small.  The  position  of  maximum 
pressure  is  not  fixed,  but  varies  with  the  resistance  encountered. 
As  a  rule  it  will  be  found  that  the  less  the  resistance  to  be  over- 
come by  the  expanding  gases  the  sooner  will  they^xert  the  maxi- 
mum pressure  and  the  less  the  maximum  pressure  will  be.  By 
the  differentiation  of  equation  (86)  we  may  obtain  the  value  for 
the  maximum,  but  it  is  too  complicated  to  be  of  practical  use. 
Examination  of  the  table  of  the  X  functions  shows  that  X3  is  a 
maximum  when  z  =  0.65,  nearly,  while  X4  and  X5  increase  indefi- 
nitely. The  functions  X%,  X4,  and  X5  are  found  to  vary  in  such 
a  manner  that  when  A,  and  therefore  N,  see  (74),  is  negative,  that 
is,  when  the  powder  burns  with  a  decreasing  surface,  p  will  be  a 
maximum  when  x  is  less  than  0.65;  and  when  X  and  N  are  positive 
or  when  the  powder  burns  with  an  increasing  surface,  p  will  be  a 
maximum  when  x  is  greater  than  0.65. 

A  function  at  or  near  its  maximum  changes  its  value  slowly. 
Therefore  a  moderate  variation  of  the  position  of  maximum  pres- 
sure will  have  no  practical  effect  on  the  computed  value  of  the 
pressure.  It  has  been  found  by  experiment  that  if  we  take  z=0.45 
for  the  position  of  maximum  pressure  when  A  is  negative,  and 
x  =  0.8  when  A  is  positive,  no  material  error  results. 

Therefore  to  obtain  the  maximum  pressure  make  x  =  0.4$,  in 
equation  (86)  when  the  powder  burns  with  a  decreasing  surface, 


90  ORDNANCE  AND  GUNNERY. 

and  make  x  =  0.8  when  the  powder  burns  with  an  increasing  sur- 
face. 

The  Pressure  P'.  —  Combining  equations  (87),  (77),  and  (73)  we 
obtain 

P'  =  —f  (89) 

' 


Comparing  this  with  equation  (45)  we  see  that  since  z0to  is  the 
initial  air  space  in  the  chamber,  P'  is  the  pressure  of  the  gases  from 
GJ  pounds  of  powder  occupying  the  volume  behind  the  projectile  before 
the  projectile  has  moved  from  its  seat.  This  volume  is  the  initial 
air  space.  Equation  (88)  is  therefore  the  equation  of  the  pressure 
curve  under  the  supposition  that  the  powder  is  all  burned  before 
the  projectile  moves. 

47.  Values  of  the  Constants  in  the  Equations  for  Velocity, 
Pressure,  and  Fraction  of  Charge  Burned.  —  We  have  now  these 
equations  which  express  the  circumstances  of  motion  of  the  pro- 
jectile, and  the  fraction  of  charge  burned*  at  any  instant.  The 
original  numbers  of  the  equations  are  given  on  the  left. 

While  the  powder  burns, 


(75)  r^MX^l  +  NXo+N'XJ}  (90) 

(86)  p  =  M'X3{l  +  NXt+N'X5\  (91) 

After  the  powder  is  burned 

(78)  vJ-VfX,  (92) 

(88)  ----  *-  (93) 


The  fraction  of  charge  burned,  substituting  N  and  N'  for  their 
values, 


(69)  -=-X«{l  +  NXo+N'X<?\  (94) 


INTERIOR  BALLISTICS.  91 

The  quantities  M,  N,  N',  M',  V1}  P'  and  X0  in  these  five  equa- 
tions are  constant  for  any  experiment,  and  their  values  must  be 
determined  before  the  equations  can  be  used.  It  will  be  seen  in 
the  equations  that  express  the  values  of  these  constants,  equations 
(74),  (77),  (85),  and  (87),  that  the  quantities  entering  the  values 
are  of  two  kinds  :  the  known  elements  of  fire  —  by  which  is  meant 
the  constants  of  the  powder,  of  the  gun,  and  of  the  projectile  —  and 
quantities  such  as  v,  X0,  X±,  etc.,  that  involve  the  velocity  and 
travel  of  the  projectile  at  the  instant  that  the  powder  is  all 
burned. 

When  M  and  N  are  known  all  the  constants  are  known. 

The  value  of  M  given  in  equation  (74)  may  be  reduced  by 
means  of  (77)  and  (71)  to 


Q  (95) 

We  have,  equation  (74), 

(96) 


M  and  N  being  known,  X0  and  Vi2  are  determined  from  these 
equations,  and  N',  Mf,  and  P'  become  known  from  (74),  (85),  and 
(87). 

Therefore  when  M  and  N  are  known  the  five  equations,  (90) 
to  (94),  are  fully  determined,  and  all  the  circumstances  attending 
the  movement  of  the  projectile  become  known  from  them.  For 
any  assumed  travel  of  the  projectile  u,  the  number  of  expansions, 
x  =  U/ZQ,  is  obtained,  and  with  this  value  of  x  the  functions  XQ  to 
X5  are  obtained  from  Table  I.  These  substituted  with  the  con- 
stants in  the  equations  give  the  values  of  v,  p,  and  y.  Proceeding 
in  this  manner  for  a  number  of  points  along  the  bore  complete 
curves  may  be  constructed  showing  the  values  of  v,  p,  and  y  for 
any  point  in  the  bore  of  the  gun. 

The  value  of  x  corresponding  to  X0  is  obtained  from  the  table. 
The  value  of  u  follows  from  the  equation  u  =  'xz0.  This  value  u 
is  the  distance  that  the  projectile  has  travelled  at  the  moment 


92  ORDNANCE  AND  GUNNERY. 

that  the  charge  is  completely  burned.  For  values  of  u  less  than 
this,  equations  (90),  (91),  and  (94)  apply;  for  greater  values  of 
u  equations  (92)  and  (93)  apply. 

48.  Determination  of  the  Constants  by  Experiment. — Regarding 
equation  (90)  and  noting  from  equations  (74)  that  N'  is  a  function 
of  N,  it  will  be  seen  that  if  we  measure  two  velocities  at  known 
points  in  the  bore  of  the  gun  we  can  determine  M  and  N  from 
equation  (90).  x  being  known  for  each  of  the  points  the  X  func- 
tions are  obtained  from  the  table.  With  the  two  measured  values 
of  v  we  then  form  two  equations  in  which  M  and  AT  are  the  only  un- 
known quantities.  Determining  M  and  N  the  other  constants 
become  known. 

In  using  this  method  care  must  be  exercised  that  the  measured 
velocities  are  taken  at  points  passed  by  the  projectile  before  the 
powder  has  completely  burned.  If  the  powder  is  not  wholly 
burned  when  the  projectile  leaves  the  gun  one  of  the  measured 
velocities  may  be  taken  at  the  muzzle. 

Since  M'  is  also  a  function  of  M,  equation  (85),  we  may  make 
use  of  the  two  equations  (90)  and  (91),  or  (92)  and  (91),  and  with 
a  single  measured  velocity  and  a  measured  pressure  determine  M 
and  N  from  these  equations.  But  it  has  been  shown  in  the  chapter 
on  powders  that  there  is  room  to  believe  that  the  pressures  as  ordi- 
narily measured  with  the  crusher  gauge  are  not  reliable.  There- 
fore results  obtained  in  this  way  are  not  likely  to  be  as  satisfactory 
as  those  obtained  from  measured  velocities,  which  can  be  deter- 
mined with  a  high  degree  of  accuracy. 

It  is  found  in  fact  that  while  the  velocities  obtained  from  the 
formulas  agree  very  closely  with  those  actually  measured  in  prac- 
tice, there  is  not  as  satisfactory  an  agreement  between  the  pres- 
sures. The  pressures  are  obtained  in  the  formulas  by  the  dynamic 
method  and  are  usually  higher  than  the  measured  pressures. 
This  is  in  accord  with  what  has  already  been  said  in  our  previous 
consideration  of  the  subject  of  pressures,  and  adds  to  the  evidence 
against  the  accuracy  of  the  crusher  gauge. 

When  T  and  /  are  known  all  the  constants  are  known. 


INTERIOR  BALLISTICS.  93 

From  equations  (63)  and  (68)  we  obtain 


From  equations  (73)  and  (77) 

f=V12w/Qga>  (98) 

from  which  can  be  determined  X0  and  Vi2.  M  and  N  follow  from 
equations  (95)  and  (96). 

T,  the  time  of  burning  of  the  whole  grain  in  air,  is  constant  for 
the  same  powder. 

The  value  of  /,  equation  (98),  is  dependent  on  the  value  of  Vif 
a  quantity  determined  by  experiment  in  the  gun.  /  for  any  pow- 
der is  therefore  constant,  within  the  limits  explained  below,  in  the 
same  gun  only.  It  is  practically  constant  for  guns  that  do  not 
differ  greatly  in  caliber.  Consequently  when  r  and  /  have  once 
been  determined  for  a  powder  and  a  gun,  we  may  at  once  form  the 
equations  of  motion  and  pressure  for  different  conditions  of  load- 
ing, involving  differences  in  the  form  and  size  of  grain  of  the  pow- 
der, in  the  weight  of  the  charge,  in  the  weight  of  the  projectile, 
and  in  the  size  of  the  chamber  and  length  of  the  gun. 

49.  The  Force  Coefficient  /.  —  The  quantity  /  at  its  first  intro- 
duction, equation  (45),  was  shown  to  be  the  pressure  exerted  by 
the  gases  from  unit  weight  of  powder,  the  gases  occupying  unit 
volume  at  the  temperature  of  explosion.  It  was  called  the  force 
of  the  powder.  But  in  the  ballistic  formulas  it  has  been  affected 
by  whatever  errors  there  are  in  the  assumptions  made  in  deducing 
the  formulas.  It  can  consequently  be  regarded  only  as  a  coeffi- 
cient, and  it  may  conveniently  be  called  the  force  coefficient. 

Its  value,  when  determined  by  experiment,  may  be  considered 
constant  in  the  same  gun  for  charges  of  the  same  powder  not 
differing  in  weight  by  more  than  about  15  per  cent  from  the 
charge  used  in  determining  its  value.  The  effective  value  of  the 
force  coefficient  is  measured  in  the  formulas  by  projectile  energy, 


94  ORDNANCE  AND  GUNNERY. 

and  there  has  been  omitted  in  deducing  the  formulas  all  considera- 
tion of  the  force  necessary  to  start  the  projectile.  As  the  charge 
decreases  the  portion  of  the  developed  force  necessary  to  start  the 
projectile  bears  a  larger  relation  to  the  total  force  exerted;  and  if 
the  charge  is  sufficiently  small  the  projectile  will  not  start  at  all. 
The  effective  force  for  a  small  charge  must  therefore  be  proportion- 
ally less  than  for  a  large  charge,  and  the  value  of  /  determined 
from  one  charge  must  be  modified  for  use  with  another  that  differs 
greatly  in  weight.  The  formula  used  by  Ingalls  for  this  modifica- 
tion will  be  found  in  equation  (137),  problem  3  of  the  applications 
which  follow. 

Values  of  the  X  Functions.  —  We  may  simplify  the  value  of 
XQ  by  means  of  circular  functions.     In  equation  (67)  make 


sec    = 
we  may  then  deduce,  see  foot-note, 

dd 


The  value  of  this  integral,  designated  as  (0),  is  given  in  Table  V 
of  the  book  of  ballistic  tables  for  every  minute  of  arc  up  to  87 
degrees.  We  therefore  have,  simply 


Differentiating  the  equation  sec  0=  (l  +  x)i 

d  sec  0  =  sec  0  tan  6  d6=  J(l  +  z)~8dz=dz/6  sec5  6 
From  the  second  and  fourth  members, 

dx=G  sec8  d  tan  d  dd 
tan  6=  (sec2  0-l)i=[(l  +  z)*-l]i 

Equation  (67)  becomes 

psec'flta 
J      sec3  6  tan  6 


INTERIOR  BALLISTICS.  95 

From  the  equations  giving  the  values  of  the  various  X  func- 
tions, (70),  (71),  and  (84),  first  making 

1 


4  0  cosec  0 
we  may  now  deduce  the  following  values: 


The  logarithms  of  the  values  of  the  -X"  functions  for  various 
values  of  x  are  found  in  Table  I  at  the  end  of  the  volume. 

The  argument  in  the  table  is  x.  The  value  of  x  is  obtained 
from  the  equation  x  =  u/Zo,  in  which  u  is  the  travel  of  the  projectile 
and  z0  the  reduced  length  of  the  initial  air  space.  Knowing  ZQ 
and  assuming  the  travel  we  obtain  x  and  from  the  table  find  the 
corresponding  values  of  the  functions. 

Interpolation,  Using  Second  Differences.  —  It  will  often  be 
necessary  in  determining  values  of  the  functions  for  values  of  x 
not  given  in  the  table  to  employ  second  differences  in  order  to  get 
the  desired  accuracy  in  the  interpolated  values  of  the  functions. 

In  a  table  containing  values  of  a  function,  the  first  differences 
are  the  differences  between  the  successive  values  of  the  function. 
The  second  differences  are  the  differences  between  the  successive 
values  of  the  first  differences.  Thus  if  the  successive  values  of 
an  increasing  function  are  a,  a',  and  a",  the  first  differences 
are  a'—  a  =  Ji,  and  a"  —  at  =  A\.  The  second  difference  is  then 

jjfc'-Jj-Ja. 

The  interpolation  may  be  effected  by  the  following  formula. 
The  sign  of  the  last  term  in  this  formula  is  made  +  so  that,  in 
this  particular  table,  only  the  numerical  values  of  the  second 
differences  need  be  considered. 


96  ORDNANCE  AND  GUNNERY. 


(99) 


in  which  x  is  the  given  value  of  the  argument,  lying  between  the 

tabular  values  xa  and  z&, 
h  =  xb—  xa, 
4i  and  J2  are  the  first  and  second  differences  of  the  func- 

tion under  consideration, 
Xa  the  tabular  value  of  the  function  corresponding  to 

Xaj 

X  the  interpolated  value  of  the  function  corresponding 
to  x. 

It  will  be  observed  that  the  difference  between  successive  values 
of  x  varies  in  different  parts  of  the  table.  In  applying  the  formula 
we  must  use  the  same  value  of  h  in  getting  the  two  first  differences 
from  which  the  second  difference  is  obtained. 

The  lower  sign  of  the  second  term  of  the  second  member  must 
be  used  when  the  function  decreases  as  x  increases.  This  sign  will 
only  be  required  for  the  values  of  the  function  Xs  when  the  value 
of  x  is  greater  than  0.65. 

EXAMPLES.  —  1.  What  is  the  value  of  log  X0  corresponding  to 

35-1.17? 

Xa-1.15       Ofc  =  1.20       /i  =  .05       X-Xa=m 

1st  diff.  2d  diff. 

X0  =  logX0(z  =  1.15)        0.52960  792  =  Al        36  =  J2 

log  X0(x  =  1.20)        0.53752  756 

log  Xa(x  =  1.25)        0.54508 
X  =  (0.52960)  +  1  792  +  f  X  f  X  36  =  (0.52960)  +  316.8  +8.6 

The  parentheses  around  0.52960  indicate  that  this  number 
is  to  be  treated  as  a  whole  number  in  applying  the  corrections. 

Therefore 

0.52960 

316.8 
8.6 


INTERIOR  BALLISTICS.  97 

2.  What  is  the  value  of  log  Xi  when  z  =  0.563? 

Ans.  Log  Xi=  9.53337. 

3.  Log  X3  for  x  =  0.275.  Log  X3  =  9.82216. 

4.  Log  X3  for  x  =  2.18.  Log  X3  =  9. 76089. 

5.  Log  X5  for  a;  =  0.772.  Log  X5  =  1.15879. 

50.  The  Characteristics  of  a  Powder. — The  quantities/,  r,  a,  A, 
and  ^  were  called  by  Sarrau  the  characteristics  of  the  powder, 
because  they  determine  its  physical  qualities.  Of  these  factors,  /, 
the  force  coefficient  of  the  powder,  depends  principally  upon  the 
•composition  of  the  powder.  In  the  same  gun  it  is  practically 
constant  for  all  powders  having  the  same  temperature  of  com- 
bustion. It  increases  with  the  caliber  of  the  gun,  and  for  this 
reason  its  value  determined  for  one  caliber  cannot  be  depended 
upon  for  another.  The  factor  T,  the  time  of  combustion  of  the 
grain  in  air,  depends  upon  the  least  dimension  of  the  grain  and 
upon  the  density;  also,  in  smokeless  powders,  upon  the  quantity  of 
solvent  remaining  in  the  powder.  The  factors  a,  A,  and  p.  depend 
exclusively  upon  the  form  of  the  grain,  and  for  the  carefully  pre- 
pared powders  now  employed  their  values  can  be  determined  with 
precision.  They  are  constant  as  long  as  the  burning  grain  retains 
its  original  form. 


APPLICATION   OF  THE   FORMULAS. 

For  convenience  of  reference  the  notation  employed  in  the 
deduction  of  the  formulas  is  here  repeated,  and  the  units  custom- 
arily employed  in  our  service  are  assigned  to  the  different  quan- 
tities. For  most  of  these  quantities  specific  units  have  not  here- 
tofore been  designated. 

a     defined  by  equation  (101)  below. 

C    volume  of  powder  chamber,  cubic  inches. 

d     caliber  in  inches. 

DI  outer  diameter  of  powder  grain,  inches. 


98  ORDNANCE  AND  GUNNERY. 

di    diameter  of  perforation  of  powder  grain,  inches. 

/      force  coefficient  of  the  powder,  pounds  per  square  inch. 

F    fraction  of  grain  burned. 

g     acceleration  clue  to  gravity,  32.16  foot-seconds. 

k  =  y/to,  fraction  of  charge  burned. 

I      thickness  of  laj^er  burned  at  any  instant,  inches. 

Zo     one  half  least  dimension  of  grain,  inches. 

L    constant  logarithms  in  the  ballistic  equations. 

m    length  of  powder  grain,  inches. 

M   ballistic  velocity  constant,  foot-seconds. 

M'  ballistic  pressure  constant,  pounds  per  square  inch. 

N,  N'  ballistic  constants. 

n     number  of  powder  grains  in  one  pound. 

Pf   ballistic  pressure  constant,  pounds  per  square  inch. 

p     pressure  while  powder  burns,  pounds  per  square  inch. 

pa   pressure  after  powder  is  burned,  pounds  per  square  inch. 

pm  maximum  pressure,  pounds  per  square  inch. 

PQ   standard  atmospheric  pressure,  14.6967  Ibs.  per  square 

inch. 

Si    initial  surface  of  a  pound  of  powder,  square  inches. 
u     travel  of  projectile,  inches. 
U    total  travel  of  projectile,  inches. 

v     velocity  of  projectile  while  powder  burns,  foot-seconds. 
va    velocity  of  projectile  after  powder  is  burned,  foot- sees. 
V    muzzle  velocity  of  projectile,  foot-seconds. 
FI  ballistic  constant,  velocity  at  infinity,  foot-seconds. 
vc    velocity  of  combustion  of  powder,  foot-seconds. 
v0    specific  volume  of  a  gas,  cubic  feet. 
VQ  initial  volume  of  a  powder  grain,  cubic  inches. 
w     weight  of  projectile,  pounds. 

x     number  of  expansions  of  volume  of  initial  air  space. 
XQ,  Xi,  X2,  X3,  X4,  X5,  functions  of  x. 
y     weight  of  powder  burned  at  any  instant,  pounds. 
z0    reduced  length  of  initial  air  space,  inches. 


INTERIOR   BALLISTICS.  99 

a  ' 

X    constants  of  form  of  powder  grain. 

P- 

3     density  of  powder. 

J  density  of  loading. 

a>  weight  of  powder  charge,  pounds. 

T  time  of  burning  of  whole  grain  in  air,  seconds. 

at  cross  section  of  bore,  square  inches. 

Quantities  topped  with  a  bar,  as  v,  x,  u,  X2,  etc.,  designate 
the  particular  values  of  the  quantities  at  the  instant  of  com- 
plete burning  of  the  powder  charge. 

With  the  units  assigned  above  the  following  working  equa- 
tions are,  with  the  aid  of  equation  (28),  derived  from  the  equa- 
tions whose  numbers  appear  on  the  left.  The  numbers  in  brackets 
are  the  logarithms  of  the  numerical  constants  after  reduction  to 
the  proper  units.  . 

(22)  J  =  [1.44217]d>/(7  (100) 

(27)  a  =  d~ 


(29)  zo  =  [1.54708]a<o/d2  (102) 

(57)  X  =  U/ZQ  (103) 

(73)  *"£  =  [4.44383]  /  X2d>/w  (104) 

(85)  M'  =  [3.828Q7]Mw/ad>  (105) 

(87)  P  =  [3.35155]Fi2w/atf  (106) 

(89)  P'  =  [1.79538]  //a  (107) 


(97)  T  =  [2.56006]v/awwX0/d2  (108) 

(98)  /  =  [5~.55617]7i2u>/d>  (109) 


100  ORDNANCE  AND  GUNNERY. 

In  addition   to   the   above  working  equations   the  following 
formulas  are  needed  or  are  useful  in  the  solution  of  most  problems. 


(74)  M^av^/X,     ]V=A/ro     N'  '  =  p/X<?  (110) 
(95)                        M  =  aV!*/X0  (111) 

(75)  ^  =  MX1\l  +  NX0+NfX02\  (112) 
(86)                        p  =  M'X3{l  +  NXi  +  N'X5}  (113) 
(78)                       va^  =  Vl2X2  (114) 

(88)  p.---  (115) 


(80)  k*>y/a)  =  v2/Vl2X1  (116) 

)'  (123) 

/ 

*o  (124) 


51.  Transformation  of  the  Formulas  into  the  Forms  (104) 

to  (109). — In  the  deduction  of  the  formulas  the  quantities 
have  been  expressed  in  general  terms,  no  units  having  been 
assigned. 

In  assigning  now  to  the  velocity  v  the  foot-second  unit  and  to 
the  weights  the  pound  unit,  we  fix  the  units  in  the  formulas  as 
the  foot,  the  pound,  and  the  second.  All  dimensional  quantities 
in  the  formulas  must  then  be  considered  as  expressed  in  feet, 
square  feet,  or  cubic  feet ;  pressures  in  pounds  per  square  foot,  and 
time  in  seconds.  As  appears  on  page  98,  we  intend  now  to  pre- 


INTERIOR  BALLISTICS.  101 

serve  the  foot-second  as  the  unit  of  velocity,  but  to  express  the 
dimensional  quantities,  such  as  d,  oj,  ZQ,  u,  etc.,  in  terms  of  the  inch 
as  the  unit,  and  the  pressures  in  pounds  per  square  inch.  We  must 
therefore  introduce  into  the  formulas  such  factors  as  will  make 
them  applicable  to  the  new  units. 

This  is  accomplished  as  follows. 

Equation  (104).  In  the  value  of  v2,  equation  (73),  g  is  already 
in  feet,  oj  and  w  in  pounds;  X2  is  dependent  only  on  x,  which  is  a 
ratio  independent  of  the  unit.  /,  which  we  now  express  in  pounds 
per  square  inch,  must,  before  being  substituted  for  /  pounds  per 
square  foot  in  (73),  be  converted  into  pounds  per  square  foot  by 
multiplying  by  144.  We  therefore  get  for  the  numerical  factor 
whose  logarithm  appears  in  (104)  the  quantity  6  g  144. 

Equation  (105).  The  quantity  ZQOJ  in  (28)  is  expressed  in 
cubic  inches,  and  before  substituting  its  value  for  ZQOJ  cubic  feet 
in  the  formulas  we  must  divide  the  value  by  1728.  This  sub- 
stitution is  made  in  equation  (85).  M'  is  a  pressure  in  pounds 
per  square  foot,  as  may  be  seen  by  substituting  for  M  its  value 
from  (74).  Equation  (85)  then  becomes  M'  =  (wv'2/2g')Xa/Xiojz0, 
work  divided  by  a  volume,  or  pressure,  see  equation  (40).  To 
reduce  M'  to  pounds  jper  square  inch  in  order  to  convert  into 
pounds  per  square  inch  the  pressures  determined  from  equation 
(86)  we  must  divide  it  by  144.  With  these  two  operations  we 
obtain,  for  the  numerical  factor  in  (105), 

17287(144X20  27.68)  =6/0  27.68 

Equation  (106).  Substitute  for  ZQOJ  in  (87)  its  value  from 
(28)  divided  by  1728,  and  divide  the  value  of  P'  by  144  to 
reduce  P'  to  pounds  per  square  inch.  The  numerical  factor  is 
2/g  27.68. 

Equation  (107).  Substitute  for  ZQOJ  in  (89);  multiply  / 
now  in  pounds  per  square  inch  by  144,  and  divide  by  144  to 
reduce  P'  to  pounds  per  square  inch.  The  numerical  factor  is 
1728/27.68. 


102  ORDNANCE  AND  GUNNERY. 

Equation  (108).    From  (97),  multiplying  and  dividing  by 


(6^0144) 
The  numerical  factor  becomes 


Equation  (109).  Reduce  (98)  to  pounds  per  square  inch  by 
dividing  by  144.  The  numerical  factor  is  l/Qg  144. 

DETERMINATION    OF   THE   BALLISTIC   FORMULAS 
FROM   MEASURED    INTERIOR   VELOCITIES. 

52.  As  a  test  of  the  formulas  that  have  been  determined,  and  at 
the  same  time  to  illustrate  their  extensive  use,  we  will  follow  Colonel 
Ingalls  in  his  application  of  these  formulas  to  the  experiments 
made  by  Sir  Andrew  Noble  in  1894  with  a  six-inch  gun.  The 
normal  length  of  the  gun  was  40  calibers,  but  it  could  be  lengthened 
as  desired  to  50,  75,  or  100  calibers. 

The  length  of  a  gun  when  expressed  in  calibers  ordinarily  means 
the  length  measured  from  the  front  face  of  the  closed  breech  block 
to  the  muzzle  of  the  gun.  The  travel  of  the  projectile  is  the  distance 
passed  over  by  the  base  of  the  projectile,  measured  from  its  posi- 
tion in  the  gun  when  loaded.  The  length  of  the  gun  in  calibers  is 
therefore  equal  to  the  travel  of  the  projectile  plus  the  length  of  the 
powder  chamber. 

By  means  of  a  chronoscope  not  differing  in  principle  from  the 
Schultz  chronoscope  that  has  been  described,  the  velocity  of  the 
shot  could  be  measured  at  sixteen  points  in  the  bore.  Noble  gives 
the  mean  instrumental  error  of  the  chronoscope  as  three  one- 
rtiillionths  of  a  second. 

Problem  i.  —  A  100-pound  projectile  was  fired  from  this  6-inch 
gun  with  a  charge  of  27J  Ibs.  of  cordite.  Diameter  of  grain  0".4, 


INTERIOR  BALLISTICS.  103 

density  1.56.    Velocities  measured  at  points  corresponding  to  the 
different  positions  of  the  muzzle  were  as  follows. 

u  =  199.2  inches  v  -  2794  f  .  s. 

259.2      "  2940    " 

409.2      "  3166    " 

559.2      "  3284    " 

The  volume  of  the  chamber  was  1384  cu.  in. 
Determine  all  the  circumstances  of  motion. 

Constants  of  the  gun.  Constants  of  the  powder. 

C  =  1384  w  =  27.5 

d  =  6  3=  1.56 

[7  =  559.2  a  =  2       j 

w  =  100  A  =  -  \    \  (see  page  21) 


From  equation  (100),        J=  0.55 

(101),  log  a  =  0.07084 
(102),  log  20=   1.50096 
00  =  31.693 

METHOD  OF  PROCEDURE.  —  With  z0  we  may  determine  from  equa- 
tion (103)  the  value  of  x  corresponding  to  any  travel  of  the  pro- 
jectile, and  with  x  we  may  obtain  from  Table  I  the  corresponding 
values  of  the  X  functions. 

We  have  now  all  the  necessary  data  for  the  solution  of  the 
problem,  and  from  this  data  we  must  determine  the  values  of 
the  constants  in  the  five  formulas  (112)  to  (116).  The  pro- 
cedure is  as  follows. 

A.  1.  Select  two  of  the  measured  velocities  and  the  corre- 
sponding values  of  the  travel  u,  and  assume  that-  the  velocities 
were  reached  before  the  powder  was  all  burned. 

2.  Substitute  successively  in  (112)  the  selected  values  of  v 


104  ORDNANCE  AND  GUNNERY, 

with  the  values  of  the  X  functions  obtained  with  the  corresponding 
travels. 

We  have  then  two  equations  in  which  only  the  constants  are 
unknown.  As  Nf  is  a  function  of  N,  there  are  but  two  constants, 
M  and  N,  to  be  determined  from  the  two  equations. 

3.  Determine  M  and  N  from  the  two  equations. 

4.  With  the  value  of  AT.  find  from  the  second  of  equations  (110) 
the  value  of  ^Y0,  and  with  this  determine  from  the  table  the  value 
of  x,  and  from  (103)  the  value  of  u. 

5.  The  powder  was    all   burned  at  this  travel  u,  and  if  the 
values  of  u  corresponding  to  the  selected  velocities  are  less  than 
u,  we  were  right  in  assuming  these  two  velocities  as  having  been 
reached  before  the  powder  was  all  burned. 

Our  determinations  of  M  and  N  are  therefore  correct,  and, 
as  explained  on  page  91,  all  the  other  constants  may  be  deter- 
mined from  these  two. 

53.  B.  If,  however,  one  or  both  of  the  selected  velocities  were 
reached  at  a  travel  greater  than  u,  our  assumption  that  they 
were  both  reached  before  the  powder  was  burned  was  wrong  and 
our  values  of  M,  N,  and  u  obtained  under  that  assumption  are 
wrong. 

We  must  therefore  determine  new  values  of  M  and  N  as 
follows. 

Substitute  the  first  of  the  selected  velocities  with  the  corre- 
sponding values  of  the  X  functions  in  (112)  as  before.  Sub- 
stitute the  second  selected  velocity  in  (114)  with  the  value  of  X2 
corresponding  to  the  travel. 

Determine  V\. 

Replace  N,  A7',  and  M  in  (112)  by  their  values  from  (110) 
and  (111).  Then  in  (112)  X0  is  the  only  unknown  quantity, 
and  its  value  can  be  determined. 

With  XQ  and  V\  the  values  of  M  and  N  are  readily 
found. 

C.  The  constants  cannot  be  determined  if  both  the  selected 
velocities  were  reached  after  the  powder  was  wholly  burned. 


INTERIOR  BALLISTICS.  105 

Equation  (114)  should  give  the  same  value  of  V\  for  both  the 
selected  velocities. 

Now  to  revert  to  the  problem,  which  will  be  solved  after  the 
first  method,  designated  A,  and  the  steps  of  the  solution  will 
be  numbered  as  in  the  explanation  above. 

We  have  to  determine  the  ballistic  constants  for  use  in  the 
velocity  and  pressure  formulas. 

Since  ^  =  0  we  see  from  equation  (110)  that 


and  that  since  A  is  negative  N  is  also  negative. 

Velocity  formula  (112)  therefore  becomes  for  this  powder 


(117) 

from  which  with  two  measured  values  of  v  and  the  correspond- 
ing values  of  u,  and  hence  of  Xi  and  X0,  we  may  determine  M 
and  N.  We  must  use  for  this  purpose  two  values  of  v  while  the 
powder  is  burning. 

1.  We  will  take  the  two  measured  values  2794  and  3166  and 
determine  afterwards  whether  we  are  right  in  the  selection. 

2.  The   X  functions   for  u  =  199.2   corresponding  to   v  =  2794 
are  found  as  follows. 

Equation  (103),  x  =  6.2853,  for  u  =  199.2. 

From  the  table  of  X  functions,  using  first  differences  only, 

log  X0  =  0.82110 

In  the  same  way  the  other  functions  for  this  value  of  x,  and 
the  functions  for  the  values  of  x  corresponding  to  the  other  given 
values  of  u,  are  obtained  from  the  table. 


u 

x 

V 

logX0 

logZ, 

logZa 

199.2 

6.2853 

2794 

0.82110 

0.50606 

1  .  68496 

259.2 

8.1784 

2940 

0.86213 

0.58011 

1.71799 

409.2 

12.9112 

3166 

0.93117 

0.69774 

1.76657 

559.2 

17.6446 

3284 

0.97710 

0.77150 

1  .  79440 

106  ORDNANCE  AND  GUNNERY. 

In  equation  (117),  using  two  values  v  and  vf  and  the  values 
of  X0  and  Xi  corresponding  to  each,  and  solving  for  N  and  M, 
we  obtain 

N= 


v2 


3.  Making  r  =  2794  and  v'  =  3166,  we  obtain  with  the  corre- 
sponding values  of  X0  and  Xi 

log  M  =  6.59155 
log  N  =  2.75465 

With  these,  as  has  been  shown  on  page  91,  all  the  other  ballistic 
constants  are  determined. 

4.  We  will  first  determine  from  the  second  of  equations  (110) 

log  X0  =  0.94432 

and  from  the  table  find  the  corresponding  value  of  x  by  inter- 
polation, using  first  differences  only, 


From  equation.  (103)  -w  =  447.19,  that  is,  the  burning  of  the 
powder  was  completed  at  the  instant  that  the  shot  had  travelled 
447.19  inches. 

5.  The  values  of  u  for  the  points  selected  for  the  determina- 
tion of  the  constants  in  the  equations  being  less  than  u  we  find 
ourselves  justified  in  the  selection  of  these  points. 

From  equation  (105)  log  M'  =4.91005 
(111)  log  VS  =  7.23484 
(106)  logP'  =5.07622 


INTERIOR  BALLISTICS.  107 

We  now  have  all  the  constants  that  enter  the  equations  (112) 
to  (116)  for  velocity  and  pressure  and  fraction  of  charge  burned. 
These  equations  become  for  this  round 

v2  =  [6.59155]Xi  (1  -  [2.75465].Y0)  (118) 

p  =  [4.91005pr3(l-[2.75465]Ar4)  (119) 

(120) 


/^2  (122) 

With  these  five  equations  we  can  determine  the  velocity, 
pressure,  and  weight  of  powder  burned  as  the  projectile  passes 
any  point  in  the  bore,  by  substituting  the  values  of  the  X  func- 
tions determined  from  Table  I  for  the  value  of  x  corresponding 
to  the  travel  of  the  projectile  at  the  point. 

In  this  way  we  find  from  equation  (118)  for  w  =  259.2,  for  which 
z  =  8.1784,  —  (the  symbol  L  indicates  a  constant  logarithm  in  the 
equation), 

logZo    0.86213 

L    2.75465 

0.41379     1.61678 


0.58621 
log^! 
L 
log  v2 
log  v 
v  = 

1.76805 
0.58011 
6.59155 

6.93971 
3.46985 
2950  foot-seconds 

This  differs  from  the  measured  velocity  by  10  feet. 

To  find  the  velocity  at  the  muzzle,  for  comparison  with  the 
measured  velocity,  we  must  make  use  of  equation  (114),  since  the 
powder  was  all  burned  before  the  projectile  reached  the  muzzle. 


108  ORDNANCE  AND  GUNNERY. 

log  V^  7.23484 

log  X2  1.79440 

log  V2  7.02924 

log  V  3.51462 

V=  3270.5  foot-seconds 

This  differs  but  13.5  feet  from  the  measured  velocity  of  3284 
feet.  The  difference,  -fa  of  one  per  cent  of  the  measured  velocity, 
is  negligible. 

In  the  same  way  the  velocity  at  any  point  may  be  determined 
and  the  curve  v  in  Fig.  20  plotted. 

54.  Pressures. — The  pressure  at  any  point  may  be  similarly 
obtained  from  equations  (119)  and  (121).  The  pressures  so  ob- 
tained are  plotted  in  the  curve  p,  Fig.  20. 

MAXIMUM  PRESSURE. — As  the  cylindrical  grain  burns  with  a 
decreasing  surface  the  maximum  pressure  is  obtained  as  explained 
on  page  89  by  making  z  =  0.45  in  equation  (119), 

for  z  =  0.45         log  X3  =  1.85640         log  X4  =  0.48444 
With  these  values  we  get  from  equation  (119) 

pm  =  48,276  Ibs. 

Weight  of  Powder  Burned. — From  equation  (122)  we  obtain 
the  curve  y,  Fig.  20,  which  shows  the  weight  of  powder  burned  at 
each  point  of  the  travel.  From  this  curve  it  is  seen  that  at  the 
point  of  maximum  pressure,  for  which  u  =  14.26  inches,  about  12 
of  the  27.5  pounds  of  the  charge  were  consumed.  The  charge  was 
half  consumed  when  the  travel  was  18  inches,  and  three-quarters 
consumed  at  a  travel  of  about  68  inches. 

The  following  table  obtained  from  the  three  equations,  (118), 
(119),  and  (122),  is  represented  by  the  curves  v,  p,  and  y  in  Fig.  20, 


INTERIOR  BALLISTICS. 


109 


c 

II 

"3 

& 

oT 
I 

I 
Q 


110 


ORDNANCE  AND  GUNNERY. 


Travel 

Veolcity 

Pressure 

Powder  burned 

X 

u 

V 

P 

y 

inches. 

ft.-secs. 

pounds. 

pounds. 

0.2 

6.34 

564.99 

43929 

8.669 

0.4 

12.67 

876.56 

48183 

11.597 

0.6 

19.02 

1109.1 

47558 

13.584 

0.8 

25.36 

1295.2 

45569 

15.097 

1.0 

31.69 

1449.8 

42895 

16.315 

1.5 

47.54 

1747.9 

36632 

18.589 

2.0 

63.38 

1967.2 

31386 

20.209 

2.5 

79.24 

2138.0 

27158 

21.442 

3.0 

95.08 

2276.1 

23738 

22.419 

4.0 

126.77 

2488.0 

18600 

23.873 

5.0 

158.46 

2644.2 

14975 

24.898 

6.2853 

199.2 

2794.0 

11642 

25.822 

8.1784 

259.2 

2950.0 

8329 

26.677 

12.9112 

409.2 

3166.0 

3840 

27.475 

14.1100 

447.2 

3198.0 

3191 

27.500 

17.6446 

559.2 

3271.0 

2411 

In  the  figure  the  curve  y  stops  at  the  travel  u  because  equation 
(122)  can  only  apply  as  long  as  the  powder  is  burning.  The  pow- 
der, wholly  burned  at  u,  is  of  course  wholly  burned  at  every  point 
beyond  u. 

The  curves  va  and  pa  in  Fig.  20  are  similarly  obtained  from 
equations  (120)  and  (121).  They  represent  the  velocity  and  pres- 
sure under  the  supposition  that  the  powder  was  wholly  burned 
before  the  projectile  moved,  and  from  them  are  obtained  the 
velocities  and  pressures  in  the  gun  after  the  powder  is  all  burned, 
that  is,  after  the  travel  u. 

The  size  of  the  page  does  not  permit  the  representation  of  the 
first  part  of  the  curve  pa-  This  curve  intersects  the  vertical  axis 
at  a  point  obtained  by  making  x==0  in  equation  (121),  for  which 
value  pa  =  119,180  Ibs.  per  sq.  in.  =  P',  see  (115).  As  explained  on 
page  90,  Pf  is  the  pressure  per  unit  of  surface  exerted  by  &  pounds 
of  powder  confined  in  a  volume  equal  to  the  initial  air  space. 

The  Force  Coefficient  /  and  Constant  T. — From  equation 

(109)  /  =2247 A  Ibs.  per  sq.  in. 
(108)  T  =  0.50486  seconds 


INTERIOR  BALLISTICS.  Ill 

/  was  originally  considered  as  the  force  of  the  powder  or,  in  the 
units  assigned,  the  pressure  exerted  by  a  pound  of  a  gas  occupying 
a  cubic  foot  at  the  temperature  of  explosion,  see  equation  (45). 
But  it  has  been  affected  by  whatever  errors  there  are  in  the  as- 
sumptions made  in  the  deduction  of  the  formulas.  It  can  conse- 
quently be  regarded  only  as  a  coefficient,  called  the  force  coefficient. 

T  is  the  total  time  of  burning  of  the  grain  in  air.  The  velocity 
of  burning  in  air  is,  therefore,  for  this  grain, 

IO/T  =  0.39615  inches  per  second. 

55.  Velocity  of  Combustion. — The  velocity  of  combustion  of 
the  powder  at  any  instant  may  be  obtained  from  equation  (61). 


by  substituting  the  value  of  p  corresponding  to  any  point  in  the 
travel  of  the  projectile.  , 

Thus  at  the  moment  of  maximum  pressure,  pm  =  48,276,  and 

vc  =  22.7  inches  per  second. 

At  this  rate  of  burning  the  charge  would  be  consumed  in  about 
nine  one-thousandths  of  a  second. 

Thickness  of  Layer  Burned. — Combining  equations  (65)  and 
(68)  we  obtain 

1  =  10X0/X0  (124) 

Substituting  for  any  point  the  value  of  X0  we  obtain  I. 
Thus  for  w  =  199.2,  log  X0  =  0.82110,  and  for  the  thickness  of 
layer  burned  at  this  travel 

1= 0.1506  inches. 

Variation  in  Size  of  Grain. — The  thickness  of  layer  burned  at 
any  travel  of  the  projectile  is  evidently  the  half  thickness  of  web 


112  ORDNANCE  AND  GUNNERY. 

of  some  whole  grain  of  the  same  shape  that  would  be  completely 
burned  at  that  point.  We  may  therefore  write  in  equation  (124) 
IQ  for  I  and  X0'  for  X0  and  form  the  equation 

210'  =  210X0'/X0  (125) 

The  web  of  a  grain  designed  to  be  completely  burned  at  any 
travel  of  the  projectile  under  the  same  conditions  of  loading  as 
in  problem  1  will  therefore  have  a  thickness  equal  to  twice  the 
thickness  of  layer  burned  at  the  travel  as  obtained  in  that  problem. 

For  u  =  199.2,     2Z0'  =  0.3012  inches, 

which  is  twice  the  value  we  found  for  I  at  this  length  of  travel. 

Variation  in  Initial  Surface  of  Charge  for  Same  Shape  of 
Grain. — From  equations  (19)  and  (125)  we  obtain 

Si'-SiXo/Xo'  (126) 

• 

For  the  grain  whose  web  we  have  just  determined  the  initial 
surface  of  the  charge  would  have  the  following  relation  to  the 
same  weight  of  charge  of  the  powder  used  in  problem  1. 

&'- 1.322  & 

56.  Variations  in  Gun,  Powder,  or  Projectile. — Having 
once  determined  the  constants  T  and  /  for  any  powder  in  a  gun 
of  any  caliber,  we  may  assume  any  variation  in  the  gun  except 
in  caliber,  or  any  variation  in  the  powder  or  in  the  projectile, 
and  determine  the  effect  of  the  variation  on  the  circumstances 
of  motion,  r,  the  time  of  complete  burning  of  the  grain  in  air,  is 
proportional  to  the  web  thickness.  Its  value  for  the  same  powder 
in  grains  of  any  other  shape  or  size  is  equal  to  the  determined 
value  multiplied  by  the  ratio  of  the  web  thicknesses  of  the  new 
grain  and  of  the  grain  used  in  the  determination.  For  any  as- 
sumed size  of  the  chamber  and  fixed  weight  of  charge  or  density 


INTERIOR  BALLISTICS.  113 

of  loading  we  may  proceed  exactly  as  in  problem  1.  For  changes 
in  the  weight  of  the  charge  or  of  the  projectile  the  procedure  is 
the  same  as  in  that  problem.  For  changes  in  the  shape  of  the 
powder  grain  the  method  to  be  pursued  will  be  best  understood 
from  an  example. 

Problem  2. — Suppose  that  the  powder  used  in  problem  1 
instead  of  being  made  up  into  cylindrical  grains  was  made  into 
ribbons  0".4  thick,  2"  wide,  and  8"  long,  of  the  same  density 
as  the  cylindrical  grains. 

Determine  the  circumstances  of  motion  with  the  same  weight 
of  charge,  27J  pounds,  as  in  that  problem. 

The  thickness  of  web,  0".4,  is  the  same  as  for  the  cordite 
cylinder. 

The  values  of  the  constants  of  form  for  the  parallelepiped 
grain  are,  see  page  19, 


x  +  y+xy 
1  +  x+y 
xy 


in  which  x  =  2lo/m  and  y  =  2lo/n. 

Making  x  =  0.4/8  =  0.05  and  y  =  0.4/2  =  0.2  we  find  for  the 
ribbon  grain  assumed  in  this  problem 

a  =  1.25,     A=- 0.208,     p  =  0.008. 

As  the  initial  surfaces  of  two  charges  of  equal  weight  com- 
posed of  the  same  powder  in  grains  of  different  shapes  are  to 
each  other  as  the  values  of  a  for  the  two  forms  of  grain,  see  equa- 
tion (19),  the  initial  surface  of  this  charge  will  be  1.25/2  =  5/8 
of  the  initial  surface  of  the  charge  in  problem  1,  and  as  the  maxi- 
mum pressure  is  dependent  upon  the  initial  surface  we  may  expect 
a  lower  maximum  pressure  from  this  charge  than  from  the  first. 

The  values  of  /  and  r  determined  in  problem  1,  being  constant 
for  the  same  powder  and  gun,  are  applicable  to  this  round,  and 
it  will  be  seen  from  equations  (100)  to  (109)  that  J,  a,  z0,  v2, 
P',  XQ,  and  Vi2  have  the  same  values  as  in  that  problem. 


114  ORDNANCE  AND  GUNNERY. 

Therefore  from  equations  (110),  (111),  and  (105)  we  obtain 
at  once  the  values  of  the  constants  in  the  formulas  for  velocity 

and  pressure. 

logM  =6.38743 

log  AT  =2.37374 

logJV'  =4.01445 

log  M'= 4.70593 

and  with  these  values  we  may  write  the  formulas  for  velocity 
and  pressure  while  the  powder  is  burning. 

v2  =  [6.38743]X1{l-[2.37374]X0  +  [4.01445]X02|, 
p  =  [4.70593]X3{l-[2.37374]X4  +  [i.01445]X5}. 

The  formula  for  the  weight  of  powder  burned  is  the  same 
as  in  problem  1,  equation  (122),  but  since  the  value  of  v  for  any 
value  of  x  is  now  different  the  weights  burned  at  the  different 
travels  will  also  be  different. 

The  formulas  for  velocity  and  pressure  after  the  charge  is  all 
burned  are  the  same  as  in  problem  1,  equations  (120)  and  (121), 
and  the  velocities  and  pressures  beyond  the  point  of  complete 
consumption  are  the  same.  The  point  of  complete  consumption 
is  the  same  as  in  that  problem,  since  X0  has  the  same  value. 

The  velocities  and  pressures  and  weight  of  powder  burned 
under  the  conditions  of  this  problem  are  shown  in  the  subjoined 
table  and  in  Fig.  21. 


Powder 

Travel 

Velocity 

Pressure 

burned 

X 

u 

V 

P 

y 

inches. 

f.  s. 

pounds. 

pounds. 

0.2 

6.34 

458.86 

29584 

5.718 

0.4 

12.67 

720.16 

33587 

7.828 

0.6 

19.02 

919.33 

34089 

9.333 

0.8 

25.36 

1081.6 

33381 

10.528 

1.0 

31.69 

1218.6 

32220 

11.527 

1.5 

47.54 

1489.7 

28926 

13.503 

2.0 

63.38 

1696.1 

25922 

15.024 

2.5 

79.24 

1862.3 

23390 

16.269 

3.0 

95.08 

2005.6 

21278 

17.326 

4.0 

126.77 

2223.2 

18001 

19.062 

5.0 

158.46 

2397.2 

15600 

20.465 

6.2853 

199.2 

2576.0 

13324 

21.947 

8.1784 

259.2 

2780.3 

10977 

23.697 

12.9112 

409.2 

3131.0 

7559 

26.871 

14.1100 

447.2 

3198.0 

7091 

27.500 

17.6446 

559.2 

3271.0 

2411 

INTERIOR  BALLISTICS. 


115 


a 


2  •-* 

^ 


116  ORDNANCE  AND  GUNNERY. 

Comparing  this  charge,  by  means  of  the  tables  or  of  the  curves, 
with  the  charge  in  problem  1  we  -see  that  while  the  muzzle  velocity 
is  the  same  the  maximum  pressure  is  reduced  from  about  48,000 
to  about  34,000  Ibs.  The  pressures  along  the  chase  are  increased. 
The  total  area  under  the  pressure  curves,  which  represent  the 
work  expended  upon  the  projectile,  must  be  equal. 

It  is  apparent  from  the  powder  curves  that  the  powder  burned 
more  progressively  in  the  second  charge  than  in  the  first.  This 
was  to  have  been  expected,  for  if  we  compare  the  rate  of  burning 
of  the  two  grains  in  air  by  means  of  equations  (9)  and  (7),  dividing 
the  half  thickness  of  web  into  five  equal  parts,  wre  find  for  the 
fraction  burned  in  each  layer: 

Cordite  grains 0.36    0.28    0.20    0.12    0.04 

Ribbon  grains 0.24    0.22    0.20    0.18    0.16 

57.  Velocities  and  Pressures  after  the  Powder  is  Burned. — 
We  have  seen,  pages  86  and  90,  that  equations  (114)  and  (115) 
are  the  equations  for  the  velocity  and  pressure  under  the  supposi- 
tion that  the  powder  is^all  burned  before  the  projectile  moves. 

The  curves  va  and  pa  in  Figs.  20  and  21  are  calculated  from 
equations  (120)  and  (121)  for  both  shapes  of  grain.  They  are 
alike  in  the  two  figures  since  the  weight  of  charge  is  the  same. 
The  curve  va,  from  equation  (120),  shows  what  the  velocities 
\\ould  be  if  the  27  J  pounds  of  powder  were  all  burned  before  the 
projectile  moved,  and  the  curve  pa  shows  the  pressures  under 
the  same  condition. 

We  find  in  practice  that  the  velocities  measured  beyond  the 
point  where  the  powder  is  all  burned  agree  with  the  velocities 
obtained  from  the  va  formula.  We  are  therefore  warranted  in 
using  this  formula  for  determining  velocities  after  the  powder 
is  burned.  And  if  the  correct  velocities  are  given  by  the  va  for- 
mula, the  pressures  obtained  from  the  pa  formula  must  also  be 
correct. 

Therefore  velocities  and  pressures  after  the  powder  is  all 
burned  are  taken  from  the  va  and  pa  curves  or  formulas. 


INTERIOR  BALLISTICS.  117 

From  the  manner  of  deduction  of  equations  (112)  and  (114) 
these  two  equations  will  give  the  same  value  v  for  the  value  u. 
The  curves  va  and  v  therefore  coincide  at  that  value  of  the  travel. 
It  will  be  observed,  however,  in  Fig.  21,  that  the  curves  pa  and  p 
for  the  ribbon  grain  do  not  coincide  at  the  travel  it. 

It  may  be  shown  analytically  that  these  curves  coincide  only 
for  grains  of  such  form  that  the  vanishing  surface  is  zero;  such 
as  the  cube,  sphere,  or  solid  cylinder,  see  page  18.  The  vanishing 
surface  of  the  ribbon  grains  of  this  problem  is  a  finite  surface 
that  suddenly  becomes  zero  at  the  travel  u.  Coincidence  of  the 
two  curves  at  this  point  could  therefore  not  be  expected. 

The  curves  pa  and  p  in  Fig.  20,  for  the  cordite  grain,  coincide 
at  u,  since  the  vanishing  surface  of  the  cordite  gi-ain  is  zero. 

58.  The  Action  of  Different  Powders. — In  Fig.  22  the  curves  of 
velocity,  pressure,  and  weight  of  powder  burned,  from  problems 
1  and  2,  are  shown  together.  This  figure  serves  well  to  illustrate 
the  action  of  different  powders  in  the  gun. 

The  curves  with  the  subscript  1  are  taken  from  problem  I, 
in  which  the  charge  was  27.5  Ibs.  of  cordite.  The  curves  with 
subscript  2  are  from  problem  2,  in  which  the  charge  was  of 
the  same  weight  as  in  problem  1  and  of  powder  of  the  same  com- 
position, but  made  up  into  ribbon-shaped  grains  with  the  same 
thickness  of  web  as  the  cordite. 

Regarding  the  curves  y\  and  y2  we  see  that  the  burning  of 
the  charge  of  powder  was  completed  in  each  case  at  the  same 
point  of  travel,  u  =  447.2  inches.  The  quantity  burned  at  any 
travel  less  than  u  was  less  for  the  ribbon  grain  than  for  the  cordite. 

The  rate  of  emission  of  gas  as  a  function  of  the  travel  of  the 
projectile  is  shown  by  the  tangents  to  the  curves  \j\  and  y2.  For 
equal  travels  of  the  projectile  the  ribbons  gave  off  gas  less  rapidly 
at  first  and  until  the  projectile  had  traveled  about  63  inches,  at 
which  point  the  curves  y\  and  y2  are  farthest  apart.  From  this 
point  on  the  ribbon  grains  emitted  gas  more  rapidly  than  the 
cordite. 

We  consequently  find  in  the  pressure  curves  lower  pressures 


118 


ORDNANCE  AND  GUNNERY. 


INTERIOR  BALLISTICS.  119 

from  the  ribbon  grains  over  this  part  of  the  bore.  The  maximum 
pressure  is  lower  and  occurs  later  than  the  maximum  pressure 
from  the  cordite.  After  the  travel  of  63  inches  the  pressure  is 
better  maintained  by  the  more  rapid  evolution  of  gas  from  the 
ribbon  grains  and  we  find  that  the  pressure  curve  p%  falls  off  more 
slowly  than  the  curve  pi,  so  that  the  two  curves  rapidly  approach 
each  other,  and  later  cross  at  a  travel  of  about  130  inches. 

At  the  instant  before  the  travel  u  is  reached  the  area  of  the 
burning  surface  of  the  ribbon  grains  has  a  considerable  value. 
It  may  readily  be  determined,  from  the  given  dimensions  and 
density  of  the  ribbon  grains,  that  there  are  76  of  these  grains 
in  the  charge  of  27 \  Ibs.  The  initial  surface  of  the  charge  is  4560 
square  inches. 

The  vanishing  surface  of  each  grain,  determined  by  mensu- 
ration or  by  making  1  =  10  in  equation  (1),  is  24.32  square  inches, 
and  for  the  76  grains,  1848  square  inches.  This  is  more  than  4/10 
of  the  original  surface. 

At  the  travel  u  this  large  burning  area  suddenly  becomes  zero. 
There  is  a  sudden  cessation  of  the  emission  of  gas  and  a  sharp 
drop  in  the  pressure.  As  the  burning  surface  of  the  cordite 
grain  approaches  zero  gradually  the  pressure  curve  pi  of  this  grain 
is  continuous. 

Since  at  the  travel  u  the  projectile  has  the  same  velocity 
from  the  two  charges,  the  work  done  upon  it  is  the  same  in  each 
case,  and  the  areas  under  the  pressure  curves  to  this  point  must 
be  equal. 

Corresponding  with  the  sudden  change  in  pressure  at  the 
travel  u  we  find  in  the  curve  v2  a  sudden  variation  in  the  rate 
of  change  of  the  velocity  of  the  projectile  as  a  function  of  the 
travel,  represented  by  the  tangent  to  the  curve. 

The  above  considerations  apply  to  the  100  caliber  length  of 
the  gun. 

Now  if  we  consider  the  gun  as  40,  50,  or  75  calibers  in  length 
neither  charge  would  have  been  wholly  consumed  in  the  bore; 
and  we  see  from  the  curves  that  m  each  case  the  muzzle  velocity 


120  ORDNANCE  AND  GUNNERY. 

would  be  less  from  the  slower  burning  powder.  It  is  therefore 
apparent  that  to  produce  in  the  gun  of  any  of  these  lengths  a  given 
muzzle  velocity,  Vi,  taken  from  the  cordite  curve,  a  larger  charge 
of  the  slower  powder  would  be  required. 

The  maximum  pr^sure  from  the  larger  charge  of  slow  powder 
would  remain  less  than  that  from  the  quicker  powder,  since  the 
area  under  the  two  pressure  curves  must  be  equal  and  the  pressure 
curve  of  the  slow  powder  would  be  the  higher  at  the  muzzle. 

As  the  gun  is  longer  the  difference  in  the  weight  of  the  two 
charges  of  the  quick  aflfd  slow  powder  that  produce  the  same 
muzzle  velocity  is  less,  until  at  some  length  the  difference  becomes 
zero.  The  advantage  of  lower  maximum  pressure  always  remains 
with  the  slower  powder. 

59.  Quick  and  Slow  Powders. — It  is  apparent  from  Fig.  22  that 
if  the  maximum  pressure  and  the  muzzle  velocities  obtained  from 
the  cordite  in  the  40  and  50  caliber  guns  are  satisfactory,  the 
muzzle  velocities  produced  by  the  same  charge  of  powder  in  the 
form  of  ribbons  would  be  too  low.  This  powder  would  be  too  slow 
for  guns  of  those  lengths,  while  for  the  guns  of  75  or  more  calibers 
it  would  be  satisfactory. 

The  powder  for  a  gun  of  any  caliber  and  length  has  the  greatest 
efficiency  when  in  grains  of  such  shape  and  dimensions  that  the 
charge  of  least  weight  produces  the  desired  muzzle  velocity  within 
the  allowed  maximum  pressure.  The  powder  that  produces 
these  results  may  be  considered  the  standard  powder  for  the 
gun. 

The  maximum  pressure  is  dependent  on  the  initial  surface  of 
the  powder  charge.  A  powder  with  greater  initial  surface  than  the 
standard  powder,  that  is  a  powder  of  smaller  granulation,  will 
produce  a  greater  maximum  pressure  and  therefore  will  be  a  quick 
powder  for  the  gun,  and  a  powder  of  larger  granulation  will  be  a 
slow  powder. 

In  powder  grains  that  are  similar  in  shape  but  of  different 
dimensions,  the  thickness  of  web  will  vary  as  the  square  root  of 
the  surface.  We  may  therefore  judge  as  to  whether  the  powder 


INTERIOR  BALLISTICS.  121 

is  quick  or  slow  for  any  gun  by  comparing  its  web  thickness  with 
that  of  the  standard  powder  of  the  same  shape. 

It  is  also  found  that  usually  a  powder  that  is  satisfactory  in  a 
gun  of  a  given  caliber  is  slow  for  a  gun  of  less  caliber  and  quick 
for  a  gun  of  larger  caliber.  Therefore,  as  has  been  shown  in  the 
chapter  on  gunpowders,  a  special  powder  is  provided  for  each 
caliber  of  gun  and  for  markedly  different  lengths  of  the  same 
caliber. 

Effects  of  the  Powder  on  the  Design  of  a  Gun. — In  the 
design  of  a  gun,  the  caliber,  weight  of  projectile,  and  muzzle  velocity 
being  fixed,  consideration  must  be  given  to  the  powder  in  order 
that  the  size  of  chamber,  length  of  gun,  and  thickness  of  walls 
throughout  the  length  may  be  determined.  We  have  seen  that  to 
produce  a  given  velocity  in  any  gun  we  require  a  larger  charge  of 
a  powder  that  is  slow  for  the  gun  than  of  a  quicker  powder.  The 
larger .  charge  will  require  a  larger  chamber  space,  and  will  thus 
increase  the  diameter  of  the  gun  over  the  chamber.  The  maximum 
pressure  being  less  than  with  the  quicker  powder  the  walls  of  the 
chamber  may  be  thinner.  The  slow  powder  will  give  higher  pres- 
sures along  the  chase,  therefore  the  walls  of  the  gun  must  here  be 
thicker.  The  weight  of  the  gun  is  increased  throughout  its 
length. 

If  we  do  not  wish  to  increase  the  diameter  of  the  chamber  we 
must,  for  the  slow  powder,  lengthen  the  gun  in  order  to  get  the 
desired  velocity. 

On  the  other  hand,  with  a  powder  that  is  too  quick  for  the  gun 
very  high  and  dangerous  pressures  are  encountered,  requiring  ex- 
cessive thickness  of  walls  over  the  powder  chamber.  The  difficul- 
ties of  obturation  are  increased.  Excessive  erosion  accompanies 
the  high  pressures  and  materially  shortens  the  life  of  the  gun. 
The  gun  may  be  shorter  and  thinner  walled  along  the  chase. 

It  is  evident  from  the  above  considerations  that  each  gun 
must  be  designed  with  a  particular  powder  in  view,  and  that  a 
gun  so  designed  and  constructed  will  not  be  as  efficient  with  any 
other  powder. 


122  ORDNANCE  AND  GUNNERY. 


DETERMINATION  OF  THE  BALLISTIC  FORMULAS  FROM 
A  MEASURED  MUZZLE  VELOCITY  AND  MAXIMUM 
PRESSURE. 

60.  In  the  previous  problems  we  determined  the  constants  in  the 
ballistic  formulas  by  means  of  measured  interior  velocities.  This 
method  will  usually  not  be  available,  as  interior  velocities  can  be 
measured  only  by  special  apparatus  not  usually  at  hand.  The 
usual  data  observed  in  firing  are  the  muzzle  velocity  and  the 
maximum  pressure. 

The  method  of  determining  the  constants  with  this  data  is 
illustrated  in  the  following  problem,  and  at  the  same  time  the 
method  of  applying  the  formulas  to  the  multiperforated  grain. 

Problem  3. — Five  rounds  were  fired  from  the  Brown  6  inch 
wire  wound  gun  at  the  Ordnance  Proving  Grounds,  Sandy  Hook 
March  14,  1905.  The  projectiles  weighed  practically  100  Ibs. 
each.  The  charge  was  70  Ibs.  of  nitrocellulose  powder  in  multi- 
perforated  grains,  with  two  igniters,  each  containing  8  ounces  of 
black  powder,  at  the  ends  of  the  charge.  The  multiperforated 
grains  weighed  89  to  the  pound.  They  were  of  the  form  described 
on  page  22.  Their  dimensions,  corrected  for  shrinkage,  were 

Di  =  0".512          d!=0".051          m  =  l".029 

The  mean  muzzle  velocity  of  the  five  rounds  was  3330.4  f.  s. 

The  measured  maximum  pressure  was  42,497  Ibs.  per  sq.  in. 

The  capacity  of  the  powder  chamber  was  3120  cubic  inches. 

The  total  travel  of  the  shot  was  252.5  inches. 

Determine  the  circumstances  of  motion. 

Before  we  can  proceed  with  the  solution  of  the  problem  we 
must  determine  the  constants  of  the  powder.  We  will  make  no 
distinction  between  the  two  different  kinds  of  powder,  but  con- 
sider the  weight  of  charge  as  71  pounds  of  multiperforated  powder. 

Dimensions  of  grains,  Di  =  0".512,     d1  =  0".051,    w=l".029. 

Weight  of  gram,  89  to  1  pound. 

We  will  first  determine  the  constants  of  form  of  the  powder 
grain. 


INTERIOR  BALLISTICS.  123 

From  equation  (13) 

21Q  =  0.08975 

and  from  equations  (12)  we  find  a  =  0.72667,  A  =  0.19590,  //  =  0.02378. 
Equation  (11),  in  which  F  is  the  fraction  of  grain  burned  when 
the  web  is  burned,  therefore  becomes  for  this  grain 

F=0.72667/-  {  1  +  0.19590^-0.02378^  1  (127) 

to  [  IQ  to  j 

Making  l  =  lo, 

F  =  0.85174  (128) 

the  fraction  of  grain  burned  when  the  burning  of  the  web  is  com- 
pleted. The  slivers  therefore  form  0.14826  of  this  particular  grain. 

FICTITIOUS  MULTI PERFORATED  GRAIN. — The  body  of  the  grain 
burns  with  an  increasing  surface,  while  the  slivers  burn  with  a 
decreasing  surface.  To  avoid  the  difficulties  that  would  follow 
from  the  introduction  of  the  two  laws  of  burning  into  the  ballistic 
formulas,  we  will  substitute  for  the  real  grain  a  fictitious  grain 
with  such  a  thickness  of  web  that  when  the  web  is  burned  the 
same  weight  of  powder  is  burned  as  when  the  whole  of  the  real 
grain  is  burned;  that  is,  the  body  of  the  fictitious  grain  is  equiv- 
alent to  the  whole  of  the  real  grain. 

For  the  body  of  the  fictitious  grain  F  in  the  formula  of  the 
fraction  burned  must  be  unity  when  1  =  1Q.  Making  F  =  l  in 
equation  (127)  and  solving  the  cubic  equation  by  Homer's  Method, 
as  explained  in  the  algebra,  we  obtain  for  1/10 

Z/Zo  =  1.1524 

The  value  of  1/10  that  will  make  J^  =  l  in  equation  (127)  can 
be  obtained  more  simply  and  with  sufficient  accuracy  by  trial  as 
follows. 

We  have  determined  that  when  1  =  10  and  Z/Z0  =  1,  F  =  0.85174. 
This  value  is  less  than  unity  by  0.148.  For  a  first  trial  we  will 
increase  the  value  of  1/10  by  0.148  and  obtain  from  (127), 

with  1/10  =  1.148  F  =  0.99568 


124  ORDNANCE  AND  GUNNERY. 

an  increase  in  the  value  of  F  of  0.144.    Therefore  if  we  further 
increase  1/1Q  by  0.005  we  will  get  a  value  of  F  near  unity; 

with  Z/Z0  =  1.153  ^  =  1.0006 

Interpolating,  by  the  rule  of  proportional  parts,  between  these  two 
sets  of  values  we  find  that  for  F  =  1 


Substituting  this  value  in  (127)  it  becomes 

1  =0.837416(1  +  0.22573-0.031581) 

Comparing  this  with  equation  (5),  1  =  a(l  +  X+  ft),  which  is  derived 
from  the  formula  for  the  fraction  burned  by  making  l  =  lo,  and 
which  expresses  the  relations  existing  between  the  constants  of 
form  of  the  powder  grain,  we  see  that  for  the  fictitious  grain 

a  =  0.837416          A  =  0.22573          /*=  -0.031581 

The  new  value  of  10  must  be  the  former  value  multiplied  by 
the  above  ratio,  1/10  =  1.1524,  since  we  have  multiplied  all  the 
quantities  in  equation  (127)  by  this  ratio  to  make  F  =  l.  There- 
fore 10  =  0.044875  XI.  1524  =  0.051714. 

The  volume  of  the  real  grain  is 

V0  =  frW  -  7di2)m  =  0.197144 

Whence  from  equation  (18)  with  n  =  89,  £  =  1.5776. 
61.  Solution.  —  We  have  now  all  the  data  necessary  for  the 
solution  of  the  problem.     For  convenience  it  is  repeated  here. 

Constants  of  the  Gun.      Constants  of  the  Powder. 

0  =  3120  d>  =     71 

d  =  Q  d=     1.5776 

U  =  252.5  a=     0.837416 

w  =  100  A=     0.22573 

Measured  Data.  p  =  -  0.031581 

V  =  3330.4  IQ=     0.051714 
pm  =  42497 


INTERIOR  BALLISTICS.  125 

From  equation  (100)        J  =  0.6299 

(101)  log  a=  1.97940 

(102)  Iogz0=   1.82144 

0o  =  66.289 

On  account  of  the  thinness  of  web  of  the  powder  grain,  and  the 
high  pressure,  we  may  be  certain  that  the  charge  was  wholly  con- 
sumed in  the  bore.  Assuming  that  the  maximum  pressure  was 
the  maximum  pressure  on  the  base  of  the  projectile  we  then  have 
a  pressure  while  the  powder  was  burning  and  a  velocity  after  the 
charge  was  all  burned.  As  explained  on  page  92,  equations  (92) 
and  (91),  or  (114)  and  (113),  are  applicable  in  this  case. 

METHOD  OF  PROCEDURE. — The  procedure  is  as  follows. 

1.  Substitute  in  (114)  the  measured  muzzle  velocity  and  the 
value  of  Xz  taken  from  the  table  with  the  value  of  x  corresponding 
to  the  travel  of  the  projectile  at  the  muzzle. 

2.  Determine  V\. 

3.  Substitute  in  (113)  the  measured  value  of  the  maximum 
pressure  and  the  values  of  the  X  functions  corresponding  to  x  =  0.8 
or  x  =  0.45,  according  as  the  grain  burns  with  an  increasing  or 
decreasing  surface. 

4.  Assume  a  value  for  the  travel  at  the  moment  of  complete 
combustion  and  determine  for  this  travel  the  values  of  x  and  .Y0. 

5.  With  this  value  of  X0  and  the  value  of  Vi,  previously  deter- 
mined, find  values  for  N,  N',  and  M'  from  (110),  (111),  and  (105). 

6.  Substitute  these  values  in  the  second  member  of  (113). 

7.  If  the  second  member  has  then  the  same  value  as  the  first 
member,  which  is  the  measured  maximum  pressure,  our  assump- 
tion of  the  travel  u  is  correct.     If  not  we  must  make  new  assump- 
tions for  u  and  determine  new  values  for  M ,  N,  and  N'  until  we 
find  values  that  will  satisfy  equation  (112). 

The  successive  steps  of  the  solution  which  follows  are  num- 
bered as  in  the  preceding  paragraph. 

1.  For  the  muzzle  U= 252.5  and,  equation  (103), 

£  =  3.8091 

From  the  table,  for  this  value  of  x 
log  X2  =  1.61019 


126  ORDNANCE  AND  GUNNERY. 

Therefore  equation  (114)  becomes  for  the  muzzle 

va2  =  (3330.4)2  =  7i2  [1.61019]  (131) 

from  which 

2.  log  7i2  =  7.43481 

3.  It  was  shown  on  page  90  that  with  a  grain  burning  with  an 
increasing  surface  the  maximum  pressure  may  be  taken  as  occur- 

ring when  t 

z  =  0.8 

which  for  this  round  corresponds  to  a  travel  u  =  53.03  inches,  see 
equation  (103). 

For  this  value  of  x  we  find  from  the  table 


log  X3  =  9.86027      log  J£4  =  0.60479      log  Z5  =  1.17352 
Equation  (113)  therefore  becomes,  since  /*  and  N'  are  negative, 

pm  =42497  =  [1.86027]M'  {  1  +  [0.60479]N-  [1.17352]JV'  }      (129) 

/ 

From  equation  (105)  we  determine  for  this  problem 

M'  =  [3.99801]  M 

and  substituting  this  value  of  M'  in  equation  (129)  it  becomes 
pm  =  42497  =  [3.85828JM  {  1  +  [0.60479]  N-  [1.17352JAT'  }       (130) 

4.  The  proper  values  of  M,  N,  and  N'  must  satisfy  equation 
(130).  But  we  see  that  equations  (110)  and  (111)  express  fixed 
relations  between  these  constants  and  V\  at  the  moment  of  com- 
plete burning  of  the  charge. 

Therefore  we  will  assume  the  travel  at  the  moment  of  com- 
plete consumption,  and  with  the  corresponding  value  of  x,  and 
therefore  of  X0,  determine  N  and  N'  from  equations  (110)  and  M 
from  (111). 

Then  substituting  this  set  of  values  in  equation  (130)  we  will 
determine  whether  the  values  satisfy  that  equation.  If  not  we 
will  make  other  assumptions  for  x  and  proceed  in  the  same  way 
until  we  find  satisfactory  values  of  the  constants. 


INTERIOR  BALLISTICS.  127 

The  value  of  x  at  the  muzzle  is  3.8091.  The  value  x  must  be 
less  than  this  since  we  are  assuming  that  the  charge  was  all  con- 
sumed in  the  gun.  Let  us  assume  x  =  2. 

5.  Taking  from  the  table   the   corresponding  value  of  log  X0 
we  find  from  equations  (110)  and  (111)  values  of  M,  N,  and  N'. 

6.  These  substituted  in  equation  (130)  make  the  second  mem- 
ber equal  to  45,746. 

7.  This  is  greater  by  3249  pounds  than  the  measured  maximum 
pressure,  42,497  pounds;   and  we  therefore  conclude  that  we  have 
assumed  a  too  rapid  combustion  of  the  powder.    The  true  value 
of  x  is  therefore  greater  than  2. 

Assume  next  _x  =  2.3 

From  the  table  log  XQ  =  0.65467 

From  equation  (111)  log  M  =6.70307 
From  equation  (110)  log  AT  =2.69892 
log  Nf  =  3.19009 

With  these  values  in  equation  (130)  we  get 
pm  =  42,909  pounds 

As  this  differs  from  the  given  pressure,  42,497  pounds,  by  less  than 
one  per  cent,  we  may  without  material  error  use  these  values  of 
the  constants  as  the  true  values. 

The  assumed  value  z  =  2.3,  by  means  of  which  the  constants 
were  determined,  gives,  from  equation  (103) 

&  =  152.5  inches 
We  have  from  equations  (105)  and  (106) 

log  M'  =  4.70108 
log  P'  =  4.95570 

We  may  now  from  equations  (112)  to  (116)  form  the  five 
equations  applicable  to  this  round. 

&  =  [6.70307]*!  { 1  +  [2.69892]X0-  [3.19009]Xo2l         (132) 
p  =  [4.70108]X8  { 1  +  [2.69892]X4-  [3.19009]Xa }          (133) 


128 


ORDNANCE  AND  GUNNERY. 


Pa~ 


[4.95570] 


(135) 
(136) 

With  these  equations  we  may  determine  the  velocity,  pressure, 
and  weight  of  charge  burned  at  any  point  in  the  bore.  For  any 
travel  less  than  152J  inches  equations  (132)  and  (133)  apply 
for  the  velocity  and  pressure,  and  equation  (136)  for  the  weight 
of  powder  burned.  For  any  travel  greater  than  152J  inches, 
equations  (134)  and  (135)  apply. 

The  table  and  curves  wrhich  will  follow  are  derived  from  these 
equations. 

A  convenient  method  of  performing  the  work  in  constructing 
the  table  or  curves  is  here  shown.  It  is  always  best  to  assume 
values  of  x  that  are  given  in  the  table,  rather  than  values  of  u, 
which  would  require  interpolation  in  the  table  to  find  the  values 
of  the  X  functions. 

The  symbol  L  in  the  following  work  is  used  to  designate  the 
various  constant  logarithms  in  equations  (132)  to  (136). 

We  will  take  for  example  the  value  £  =  0.8,  corresponding  to 
the  travel  at  which  we  found  the  maximum  pressure. 

From  the  table: 


log  X0  =  0.46075 
log  X3  =  9.86027 

Equation  (103) 


log  Xi  =  9.71  100 
log  X4  =  0.60479 


log  X2  =  9.25025 
log  X5  =  1.17352 


Equation  (132) 

log  Xl     1.71100 

logM     6.70307 

6.41407  

0.05365. 1.13150 

log  v2      6.46772 

log  v       3.23386 

v  =  1713.4  foot  seconds 


log  x    1.90309 
logzo     1.82144 

log  u    1.72453 

u  =  53.031  inches 

logXo    0.46075 
log  N      2.69892 

1.15967 

logAV  0.92150 

+  1          1.14443 

log  Nf     3.19009 

0.01293  .  . 

2.11159 

INTERIOR  BALLISTICS.  129 

Equation  (133)  log  X4  0.60479 

L  2.69892 

logZ3     1.86027  1.30371          log  X5    1.17352 

logM'     4.70108          +1  1.20124          log  N'     3.19009 

4.56135  0.02310 2.36361 

0.07120 1.17814 

log  pm     4.63255 

pm=  42909  Ibs.  per  sq.  in. 


y  =  43.045  Ibs. 


Equation  (136) 

log  v2      6.46772 
L      6.41645 
cologX2    0.74945 

log  y       1.63392 

And  if  we  desire  the  values  of  va  and  pa, 


Equation  (134)     log  F,2     7.43481  Equation  (135)    log  1.8     0 . 25527 

logX2      j .  25025  X4/3       0.34036 

log  Va.2     6.68586  log  P'      4.95570 

Iogv0       3.34253  log  pa      4.61534 

t>g=2200.5  f.  s.  pa=41,242  Ibs.  per  sq.  in. 

These  values  of  va  and  pa  are  what  the  velocity  and  pressure 
would  have  been  had  the  powder  all  burned  before  the  projectile 
moved. 

The  calculations  for  velocity  and  pressure  at  any  point  of 
the  bore  beyond  the  point  of  complete  combustion  of  the  charge 
are  extremely  simple,  being  limited  to  the  solving  of  the  two 
equations  (134)  and  (135),  which  require  from  the  table  the 
function  X2  only. 

Proceeding  as  above  for  different  values  of  x  we  obtain  the 
data  collected  in  the  table  on  page  130,  from  which  the  curves 
in  Fig.  23  are  constructed. 

62.  Pressure  Curves  for  Real  and  Fictitious  Grains. — We 
have  used  in  the  deduction  of  the  equations  from  which  the  table 
is  produced  a  fictitious  multiperforated  grain  the  body  of  which, 
without  the  slivers,  equals  the  whole  of  the  real  grain.  The 
body  of  the  real  grain  was,  as  shown  by  equation  (128),  85.174 
per  cent  of  the  whole  grain,  the  slivers  forming  14.826  per  cent 
of  the  whole.  The  table  and  curve  p  show  discontinuity  of 


130 


ORDNANCE  AND  GUNNERY. 


0.0 
0.1 
0.2 
0.4 
0.6 
0.8 
1.0 
1.3 
1.6 
1.9 
2.3 
3.1 
3.8091 


40  - 


30 


Travel 

u 

inches. 

0.00 

6.63 

13.26 

26.52 

39.77 

53.03 

66.29 

86.18 

106.06 

125.95 

152.47 

205.50 

252.50 


Powder 
burned 


00.00 
15.02 
21.43 
30.48 
37.35 
43.05 
47.98 
54.43 
60.04 
65.04 
71.00 


Velocity    Pressure      Velocity    Pressure 


v 

f.  8. 

000.0 
424.3 
695.9 
1113.4 
1440.8 
1713.4 
1947.9 
2248.9 
2505.3 
£729.1 
2989.2 


P 
Ibs. 

00000 
26018 
33698 
40316 
42500 
42909 
42500 
41223 
39659 
38052 
36002 


f.  s. 
000.0 
922.5 
1266.8 
1699.2 
1986.5 
2200.5 
2369.5 
2568.6 
2724.5 
2851.4 
2989.2 
3195.4 
3330.4 


Ibs. 
90300 
79525 
70814 
57657 
48254 
41242 
35836 
29742 
25258 
21836 
18380 
13761 
11124 


.30 


II.  / 

L 

Vertical 

f 
scales,  v 

y 

1000  Ibs.  ^>. 
100  f.s.      ^\^ 
2  Ibs. 

~      '   \ 

f 

1 

26.5        53.0  106.0  152.5        Travel,  Inches.        2525 

FIG.  23. — Charge,  71  pound",  Mult  {perforated  Grains. 


INTERIOR  BALLISTICS.  131 

the  pressure  at  the  travel  152.5  inches  when  the  burning  of  the 
whole  charge  is  completed. 

Actually  there  is  no  discontinuity  in  the  true  pressure  curve. 
The  web  of  the  real  grain  was  burned  when  85.2  per  cent  of  the 
body  of  the  fictitious  grain,  or  of  the  whole  charge,  was  burned. 
This  portion  of  the  charge,  60.5  Ibs.,  was  burned  at  a  travel  of 
about  109  inches,  as  may  be  seen  from  the  table.  The  charge 
burned  with  an  increasing  surface  up  to  this  point  of  travel  and 
then  with  a  decreasing  surface  which  gradually  approached  the 
vanishing  surface  zero. 

The  pressure  would  therefore,  at  a  travel  of  109  inches,  begin 
to  fall  off  more  rapidly,  making  a  point  of  inflection  in  the  true 
pressure  curve.  From  this  point,  as  the  slivers  burn,  the  pressure 
curve  should  gradually  approach  the  curve  pa  and  join  it  at  some 
point  beyond  the  theoretical  u  =  152.5  inches,  since  the  slivers, 
burning  with  a  constantly  decreasing  surface,  will  require  a  longer 
time  for  complete  consumption  than  the  same  weight  in  the 
body  of  the  fictitious  grain. 

The  Constant  T  for  this  Powder. — From  equation  (108), 

T  =  0.37477  seconds 

This  is  the  time  of  burning  of  the  whole  grain  in  air. 

The  velocity  of  burning  of  this  grain  in  air,  IQ/T,  =0.138  inches 
per  second. 

The  velocity  of  combustion  in  the  gun  is  given  by  equation 
(123),  and  the  thickness  of  layer  burned  at  any  travel  by  equa- 
tion (124). 

The  Force  Coefficient  /.—From  equation  (109), 

/  =  1379.5  Ibs.  per  sq.  in. 

It  has  been  previously  stated  that  /  is  constant  for  any  powder 
in  a  given  gun  for  charges  not  differing  greatly  in  weight.  The 
effective  value  of  /,  as  measured  in  the  formulas  by  projectile 
energy,  must  decrease  as  the  charge  decreases,  for  we  have  omitted 
in  the  formulas  all  consideration  of  the  force  necessary  to  start 
the  projectile.  It  is  apparent  that  if  the  charge  were  sufficiently 


132  ORDNANCE  AND  GUNNERY. 

reduced  the  projectile  would  not  move,  and  /  in  the  iormula  would 
be  zero. 

Therefore  for  any  charge  differing  materially  in  weight  from 
the  charge  used  in  the  determination  of  /  the  value  of  /  must  be 
modified. 

Ingalls  adoots  Provisionally,  this  relation. 

V 


>-/•(£)*  (137) 


in  which  <LQ  is  the  weight  of  charge  used  in  the  determination  of 
/0;  /is  the  modified  value  of  /o  for  the  charge  o>;  a>  is  any  charge 
differing  in  weight  from  the  charge  a>0  by  15  per  cent  or  more. 

The  value  of  /  will  be  modified  also  by  a  marked  change  in 
the  weight  of  the  projectile.  Ingalls  uses  for  /  in  this  case  the 
value 


and  if  both  A  and  w  change  sufficiently, 


CD0 

With  the  modified  value  of  /  from  equation  (137)  we  may 
now  determine  the  velocities  produced  by  reduced  charges. 

63.  Problem  4.  —  What  muzzle  velocities  should  be  expected 
from  the  6  inch  gun  of  problem  3,  with  charges  (including  igniters) 
.of  59  and  33  £  Ibs.  of  the  powder  used  in  that  problem? 

As  these  charges  differ  in  weight  by  more  than  15  per  cent 
•of  the  charge  of  71  Ibs.  used  in  problem  3,  we  will  obtain  the 
value  of  /  from  equation  (137),  using  for  d>0  and  /0  the  values 
of  problem  3. 

We  have  as  before 

C  =  3120          5  =  1.5776          17  =  252.5 
The  work  may  !>>  conveniently  performed  as  follows. 


INTERIOR  BALLISTICS. 


133 


Charge,  59  Ibs. 

Equation  (137)   log  &      1.77085 
log  (!>Q     1.85126 


-3 

log/o 
I*/ 


1.91959 
1.97320 
3.13972 


3.11292 

Equation  (109)   log  <D/W  1.77085 

L      4.44383 

log  7i2    7.32760 

(100)    A  =0.5234 


Equation 
Equation 
Equation 


(101)  log  a    =0.10605 

(102)  log  z0  =1.86768 

z0  =73.736 

Equation  (103)  for  the  muzzle, 
x    =3.4244 

From  the  table   log  X2    1.59202 

Equation  (114)  log  Fi2  7.32760 
logva2  6.91962 
log  va  3.45981 

F  =  2883f.s. 


Charge,  33\  Ibs. 
1.52179 
1.85126 

1.67053 
1.89018 
3.13972 
3.02990 

1.52179 

4.44383 
6.99552 

0.2950 
0.44028 

1.95285 
89.712 


2.8146 
1.55630 

6.99552 
6.55182 
3.27591 

=  1888f.  s. 


The  muzzle  velocities  actually  obtained  with  charges  of  the 
above  weights  were  2879  and  1913  f.  s.  respectively.  The  calcu- 
lated velocities  show  differences  of  4  and  25  f .  s.  respectively. 
The  latter  difference,  though  practically  not  very  great,  shows 
that  the  modified  value  of  /  determined  from  the  value  deduced 
from  one  charge  gives  only  approximate  results  when  the  second 
charge  is,  as  in  this  case,  less  than  47  per  cent  of  the  first. 

64.  Problem  5. — What  muzzle  velocities  should  be  expected 
from  the  6  inch  gun  of  problem  3,  with  charges  (including  igniters) 
of  68  and  75  Ibs.  of  the  powder  used  in  that  problem? 

As  these  charges  differ  but  little  in  weight  from  the  charge 
of  71  Ibs.  used  in  problem  3,  the  value  of  /  there  determined  will 
serve  in  this  problem. 


134 


ORDNANCE  AND  GUNNERY. 

=  1379.5      C  =  3120,     <5  =  1.5776      17  =  252.5 


Charge,  68  Ibs. 
Equation  (100)  J=  0.6033 

Equation  (101)      log  a  =0.01016 
Equation  (102)      log  z0  =  1  .83344 


Equation  (103)  x  =3.7052 

Equation  (109)  log  TV  =  7.41606 

From  the  table  log  X2  =  1.60555 
Equation  (114)  7=3242f.  s. 


Charge,  75  Ibs. 
0.6654 

1.93901 

1.80486 
63.806 

3.9573 
7.45861 
1.61648 
7  =  3448f.  s. 


The  measured  muzzle  velocities  with  these  charges  were, 
respectively,  3236  and  3255  f.  s.  The  differences  between  the 
calculated  and  measured  velocities  are  immaterial. 

We  may  make  for  this  powder  and  gun  any  desired  assump- 
tion as  to  the  form  of  the  powder  grain,  weight  of  charge,  weight 
of  projectile,  size  of  powder  chamber  or  length  of  gun,  and  with 
the  values  of  /  and  T  from  problem  3,  determine  the  full  circum- 
stances of  motion  under  the  assumption. 

Sufficient  illustration  has  now  been  given  of  the  remarkable 
accuracy,  the  simplicity  and  extensiveness  of  application  of  the 
ballistic  formulas  deduced  by  Colonel  Ingalls.  By  their  use  we 
may  obtain  a  more  intimate  knowledge  of  the  conditions  existing 
in  the  bore  of  a  gun  than  has  heretofore  been  attainable;  and 
the  knowledge  so  obtained  will  be  applied  in  the  manufacture  of, 
powder  and  of  guns,  and  will  result  in  the  production  of  more 
efficient  weapons. 

United  States  Army  Cannon. — A  table  containing  data  con- 
cerning the  principal  cannon  now  in  service  follows.  The  bursting 
charges  for  projectiles  as  given  in  the  table  are  of  rifle  powder 
for  the  1.457  inch  and  3.2  inch  guns,  the  3.6  inch  mortar,  the 
6  inch  howitzer,  and  the  two  subcaliber  tubes.  For  all  other 
projectiles  the  bursting  charges  are  of  high  explosive. 


INTERIOR  BALLISTICS. 


135 


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CHAPTER  IV. 
EXPLOSIVES. 

65.  Explosive  and  Explosion. — An  explosive  is  a  substance 
that  is  capable  of  sudden  change  from  a  solid  or  liquid  state  to  a 
gaseous  state,  or  a  mixture  of  gases  whose  chemical  combination, 
suddenly  effected,  results  in  a  great  increase  of  volume.  A  chem- 
ical explosion  is  always  attended  by  the  emission  of  great  heat. 

An  explosion  due  to  physical  causes  alone,  as  when  a  gas  under 
compression  is  suddenly  released  and  allowed  to  expand,  causes 
cold. 

Effects  of  Explosion. — The  effects  of  an  explosion  are  depend- 
ent on  the  quantity  of  gas  evolved,  on  the  quantity  of  heat,  and 
on  the  rapidity  of  the  reaction. 

QUANTITY  OF  GAS.  PRESSURE. — The  volume  of  gas  at  the 
temperature  of  explosion  determines  the  pressure  exerted  against 
the  walls  of  the  vessel  containing  the  explosive. 

Force. — The  pressure  per  unit  of  surface  exerted  by  the  gases 
from  unit  weight  of  the  explosive,  the  gases  occupying  unit  volume 
at  the  temperature  of  explosion,  is  called  the  force  of  the  explosive. 
The  unit  volume  occupied  by  the  gases  is  exclusive  of  the  co- 
volume  of  the  gases  and  the  volume  of  any  residue. 

QUANTITY  OF  HEAT.  WORK. — The  quantity  of  heat  determines 
the  quantity  of  work  that  may  be  effected  by  the  explosion.  The 
bursting  of  the  walls  of  the  containing  vessel  and  the  projection 
of  the  fragments,  or  the  projection  of  the  shot  from  a  gun,  are 
effects  produced  by  the  conversion  of  the  heat  of  explosion 
;nto  work. 

Potential. — The  total  work  that  can  be  performed  by  the 
gas  from  unit  weight  of  the  explosive  under  indefinite  adiabatic 
expansion  measures  the  potential  of  the  explosive. 

136 


EXPLOSIVES.  137 

The  theoretical  potential  of  an  explosive  is  never  reached  in 
practice.  The  potentials,  however,  afford  the  means  of  comparing 
the  maximum  theoretical  quantities  of  work  to  be  obtained  from 
different  explosives.  The  maximum  practical  effect  obtained 
from  explosives  in  firearms  is  from  ^  to  ^  of  the  potential. 

RAPIDITY  OF  REACTION. — An  explosion  starts  with  the  ex- 
plosion of  a  single  molecule,  or  particle,  of  the  explosive.  The  heat 
generated  and  the  shock  developed  by  the  explosion  of  the  first 
molecule  are  communicated  to  the  surrounding  molecules  and  by 
the  explosion  of  these  molecules  are  transmitted  further  into  the 
mass. 

The  rapidity  with  which  the  explosive  reaction  is  transmitted 
through  the  mass  varies  greatly  in  different  explosives. 

The  explosion  of  gunpowders  does  not  differ  in  principle  from 
the  burning  of  a  piece  of  wood  or  other  combustible.  As  we  have 
seen  in  the  chapter  on  gunpowders  the  combustion  proceeds  from 
layer  to  layer  and  the  rate  of  combustion,  in  air  and  in  the  gun, 
and  the  quantity  of  powder  burned  at  any  time,  may  be  deter- 
mined by  means  of  the  formulas  of  interior  ballistics. 

The  explosion  of  nitroglycerine,  of  guncotton,  and  of  other 
explosives  of  like  nature  is  effected  with  very  much  greater 
rapidity  than  the  explosion  of  gunpowder.  The  theory  of  Berthelot 
is  that  in  these  explosives  the  spread  of  the  explosive  reaction  is 
not  confined  to  the  exposed  surfaces,  but  that  the  explosion  of  the 
initial  molecule  gives  rise  to  an  explosive  wave  which  is  trans- 
mitted with  great  velocity  in  all  directions  through  the  mass 
and  causes  the  almost  instantaneous  conversion  of  the  whole 
body  into  gas.  The  velocity  of  propagation  of  the  explosive  wave 
through  a  mass  of  guncotton  has  been  determined  experimentally 
by  Sebert  to  be  from  16,500  to  20,000  feet  per  second. 

The  progressive  emission  of  gas  from  gunpowder  produces  a 
propelling  effect  by  causing  a  gradual  increase  of  pressure  on  the 
base  of  the  projectile,  while  the  sudden  conversion  into  gas  of  nitro- 
glycerine or  guncotton  produces  the  effect  of  a  blow  of  great  in- 
tensity. 

66.  Orders  of  Explosion. — The  differences  in  the  rapidity  of 
reaction  give  rise  to  the  division  of  explosives  into  two  groups, 
high  explosives  and  low  or  progressive  explosives.  Explosions 


138 


ORDNANCE  AND  GUNNERY. 


are  designated  as  detonations  or  explosions  of  the  first  order, 
and  progressive  explosions  or  explosions  of  the  second  order. 

The  high  explosives  are  those  of  great  rapidity  of  reaction. 
Their  complete  explosions  are  of  the  first  order,  and  produce  by 
reason  of  their  quickness  a  crushing  or  shattering  effect  on  any 
material  exposed  to  them. 

The  principal  high  explosives  in  general  use  are  nitroglycerine, 
the  dynamites,  guncotton,  picric  acid  and  its  salts,  the  Sprengel 
mixtures,  and  the  fulminate  of  mercury. 

The  cadets  of  the  Military  Academy  have  studied  in  their 
course  in  chemistry  (Descriptive  General  Chemistry  (Tillman), 
pages  369  to  385)  the  constitution,  method  of  production,  and 
characteristics  of  the  principal  high  explosives.  It  is  therefore 
unnecessary  to  further  describe  these  explosives  here. 

The  progressive  explosives  are  those  that  consume  an  appreciable 
time  in  the  explosion.  They  produce  explosions  of  the  second 
order.  The  explosion  is  slow,  comparatively,  and  progressive,  and 
produces  a  propelling  or  pushing  effect. 

The  various  gunpowders  are  progressive  explosives.  Gun- 
powders have  been  fully  described  in  Chapter  I. 

Nitrocellulose. — The  classification  by  Vielle  of  the  nitrocellu- 
loses  of  various  degrees  of  nitration  is  shown  in  the  following  table. 
The  higher  the  degree  of  nitration  of  the  cellulose  the  greater  is 
the  power  of  its  explosion. 

VIELLE'S  CLASSIFICATION  OF  NITROCELLULOSES. 


Formula. 

Designation. 

c.c.  of 
NO2. 

Per  Cent 
of  N. 

Remarks. 

C24H360^(N02)4 

Tetra-n.c. 

108 

6.76 

Penta- 

128 

8.02 

CUH.A.CNOIX 

Hexa- 

146 

9.15 

Only  slightly  attacked  by 

acetic  ether    and    ether- 

a  73 

alcohol. 

3  § 

C24H33Ojo(NO2)7 

Hepta- 

182 

10.18 

Becomes      gelatinous      in 

•p? 

acetic   ether   and   ether- 

fe  8 

alcohol. 

€24H32020(NOS)I1 

Octo- 

178 

11.11 

Soluble  in  ether-alcohol.    Inferior 

colloid. 

054113,020  (NO,)9 

Ennea- 

190 

11.96 

\  Highly  soluble  in  ether-alcohol. 

C^HaoOjoCNOj),,, 

Deca- 

203 

12.75 

/      Superior  colloid. 

C24  H^Oa,  (NO2  )  j  , 

Endeca- 

214 

13.47 

Insoluble  in  ether-alcohol. 

Solu- 

ble  in  acetone.     Guncotton. 

EXPLOSIVES.  139 

It  will  be  observed  that  the  general  formula  for  nitrocellulose 


The  last  four  nitrocelluloses  of  the  table  are  used  in  the  manu- 
facture of  gunpowders. 

67.  Conditions  that  Influence  Explosions.—  The  character  of 
the  explosion  produced  by  any  explosive  is  influenced  by  the 
physical  condition  of  the  explosive,  by  the  external  conditions, 
and  by  the  nature  of  the  exciting  cause. 

PHYSICAL  CONDITION.  —  The  influence  of  the  physical  condition 
of  the  explosive  is  seen  in  the  sputtering  of  damp  black  powder 
when  ignited,  and  in  the  insensitiveness  to  explosion  of  nitro- 
glycerine when  frozen. 

EXTERNAL  CONDITIONS.  —  External  conditions  influence  the 
explosion  chiefly  by  the  amount  of  confinement  they  impose. 
Confinement  is  necessary  to  obtain  the  full  practical  effect  of  all 
explosives.  The  more  rapid  the  reaction  the  less  the  degree  of 
confinement  required.  Thus  blocks  of  iron  may  be  broken  by  the 
explosion  of  nitroglycerine  upon  their  surfaces  in  the  open  air.  In 
this  case  the  air  imposes  sufficient  confinement,  as  the  explosion  is 
so  quick  that  its  effect  on  the  iron  is  produced  before  the  air  has 
time  to  move. 

Gunpowder,  on  the  other  hand,  requires  strong  confinement  if 
its  complete  explosion  is  desired.  Thus,  in  firing  a  large  charge 
of  gunpowder  under  water,  unless  the  case  is  strong  enough  to 
retain  the  gases  until  the  reaction  is  complete  the  case  will  be 
broken  by  the  pressure  of  the  gases  first  given  off,  and  a  por- 
tion of  the  charge  will  be  thrown  out  unburned.  Large  powder 
grains  are  frequently  thrown  out  of  the  gun  not  wholly 
burned. 

The  confinement  required  by  the  slower  explosives  may  be 
diminished  by  igniting  the  charge  at  many  points,  so  that  less 
time  is  required  for  the  complete  explosion. 

EXCITING  CAUSE.  —  Heat  is  the  immediate  cause  of  all  explo- 
sions, whether  communicated  to  the  explosive  directly  by  a  flame 
or  heated  wire,  or  indirectly  through  friction,  or  percussion,  or 
chemical  action.  Each  explosive  has  a  specific  temperature  of 
explosion,  to  which  one  or  more  of  the  molecules  must  be  raised 
before  the  explosion  can  begin.  The  heating  of  the  initial  mole- 


140  ORDNANCE  AND  GUNNERY. 

cule  to  the  exploding  point  is  not  of  itself  sufficient  to  cause  ex- 
plosion of  the  entire  mass,  but  this  temperature  must  be  trans- 
mitted from  molecule  to  molecule  throughout  the  mass. 

The  method  of  producing  the  explosion  of  the  initial  molecule 
has  with  many  explosives  an  important  influence  on  the  character 
of  the  explosion.  Nitroglycerine  when  ignited  in  small  quantities 
burns  quietly,  but  when  struck  it  explodes  violently.  Similarly, 
guncotton  when  ignited  by  a  flame  burns  progressively  and  the 
combustion  may  be  extinguished  by  water,  but  when  detonated 
by  an  explosive  cap  the  explosion  is  of  the  first  order.  Most  of  the 
high  explosives  produce  either  detonations  or  explosions  of  lower 
order,  depending  upon  the  manner  in  which  the  explosion  is  ini- 
tiated, and  it  is  stated  by  Roux  and  Sarrau  that  even  black  gun- 
powder may  be  detonated  by  the  use  of  nitroglycerine  as  an  ex- 
ploding charge. 

Flame  is  sufficient  to  cause  the  complete  explosion  of  the  pro- 
gressive explosives,  though  it  may  be  necessary  with  some  explo- 
sives that  the  flame  be  continuously  applied.  For  some  qf  the 
high  explosives  a  percussive  shock  suffices  to  induce  an  explosion 
of  the  first  order,  while  other  high  explosives  are  practically  in- 
sensitive to  shock  and  require  for  their  explosion  an  initial  explo- 
sion of  some  detonating  substance. 

68.  Uses  of  Different  Explosives. — It  is  apparent  from  what 
has  been  said  concerning  the  differences  in  rapidity  of  reaction  of 
the  various  explosives  and  the  influences  of  external  conditions 
that  each  class  of  explosives  has  its  particular  field  of  usefulness. 

Thus  the  progressive  explosives  are  more  suitable  for  use  in 
guns  where  a  propelling  rather  than  a  shattering  effect  is  desired 
from  the  explosion.  A  high  explosive  acts  so  quickly  that  if  used 
in  a  gun  its  explosion  would  be  completed  practically  before  the  pro- 
jectile moved,  with  the  result  that  the  whole  of  its  enormous  force 
would  be  exerted  upon  the  walls  of  the  gun  to  produce  rupture. 

For  the  movement  of  masses  of  earth  the  slow  explosive  is 
better  than  the  more  rapid  one,  for  here  also  a  propelling  rather 
than  a  shattering  effect  is  desired. 

In  submarine  mines  the  best  results  are  obtained  from  dynamite 
No.  1,  a  dynamite  consisting  of  75  parts  by  weight  of  nitroglyc- 
erine absorbed  into  the  pores  of  25  parts  of  the  siliceous  earth 


EXPLOSIVES.  141 

called  kieselguhr.  The  effect  of  the  inert  substance  is  to  retard 
the  explosion  of  the  nitroglycerine,  and  the  retarded  explosion  is 
of  greater  effect  in  a  yielding  substance  like  water  than  the  more 
rapid  explosion  of  pure  nitroglycerine. 

In  hard  rocks  and  metals  the  quickest  explosive  will  give  the 
best  results,  as  in  these  hard  substances  the  greatest  intensity  of 
blow  is  required  to  produce  the  shattering  effect  desired.  Dyna- 
mite is  ordinarily  used  for  blasting  purposes  on  account  of  its  con- 
venient form,  its  comparative  safety  in  handling,  and  its  ease  of 
ignition. 

Bursting  Charges  in  Projectiles. — The  explosives  used  as  burst- 
ing charges  in  armor  piercing  projectiles  must  have  a  great  shatter- 
ing effect  in  order  to  break  the  projectile  into  fragments  and  to 
project  the  fragments  with  force;  and  at  the  same  time  the  ex- 
plosive must  be  practically  insensitive  to  shock,  so  that  it  will 
not  be  exploded  by  the  shock  of  discharge  in  the  gun  or  the  shock 
of  impact  on  the  ship's  armor.  The  explosion  of  the  bursting 
charge  of  an  armor  piercing  projectile  is  effected  by  a  detonating 
fuse  so  arranged  as  to  cause  the  projectile  to  burst  after  it  has 
perforated  the  armor. 

The  explosives  used  by  the  various  foreign  nations  as  bursting 
charges  in  projectiles  are  all  composed  principally  of  picric  acid 
or  its  derivatives.  The  French  melinite,  the  English  lyddite,  the 
Japanese  shimose  powder  are  examples. 

Some  of  the  picrates,  as  the  picrates  of  lead,  calcium,  mercury, 
and  others,  are  more  sensitive  to  friction  and  percussion  than 
picric  acid  itself.  In  order  to  prevent  the  formation  by  chemical 
action  of  any  of  these  sensitive  compounds  when  the  bursting 
charge  is  composed  of  picric  acid  or  of  any  of  its  derivatives,  the 
walls  of  the  projectile  and  all  metal  parts  that  come  in  contact 
with  the  bursting  charge  are  covered  with  a  protecting  coat  of 
rubber  paint. 

The  walls  of  the  cavity  of  the  shell,  the  base  plug,  and  the 
body  of  the  fuse  are  so  painted;  also  the  screw  threads  of  the  base 
plug  and  fuse.  Red  or  white  lead  or  other  metal  lubricant  must 
not  be  used  on  the  screw  threads. 

69.  Requirements  for  High  Explosives  for  Projectiles.— 
The  following  requirements  are  considered  essential  for  a  high 


142  ORDNANCE  AND  GUNNERY. 

explosive  to  be  used  in  filling  shell.  They  have  been  found  neces- 
sary as  a  result  of  a  long  series  of  tests. 

SAFETY  AND  INSENSITIVENESS. — The  explosive  should  be 
reasonably  safe  in  manufacture  and  free  from  very  injurious  effects 
upon  the  operatives. 

It  must  show  a  relatively  safe  degree  of  insensitiveness  in  an 
impact  testing  apparatus. 

It  must  withstand  the  maximum  shock  of  discharge  under 
repeated  firings  in  the  shells  for  which  it  is  intended. 

It  must  withstand  the  shock  of  impact  when  fired  in  unfused 
shell,  as  follows: 

(a)  Field  Shell. — With  maximum  velocity,  against  3  feet  of 
oak  timber  backed  by  sand.  With  the  remaining  velocity  for  full 
charge  at  1000  yards  range,  against  a  seasoned  brick  wall. 

(6)  Siege  Shell. — Against  seasoned  concrete  thicker  than  the 
shell  will  perforate  with  remaining  velocity  for  full  charge  at 
500  yards  range. 

(c)  Armor  Piercing  Shell. — Against  a  hard  faced  plate  of 
thickness  equal  to  the  caliber  of  the  projectile. 

DETONATION  AND  STRENGTH. — It  must  be  uniformly  and 
completely  detonated  with  the  service  detonating  fuse. 

It  should  possess  the  greatest  strength  compatible  with  a 
satisfactory  fragmentation  of  the  projectile.  The  average  frag- 
ment of  a  projectile  should  be  effective  against  the  vulnerable 
material  of  a  ship,  such  as  the  mechanisms  of  guns,  gun  mounts, 
engines,  boilers,  electric  installations,  and  the  like.  With  very 
quick  and  powerful  explosives,  as  explosive  gelatin  and  picric 
acid,  the  shattering  effect  is  excessive  and  the  fragments  of  the  pro- 
jectile are  too  small. 

STABILITY. — It  must  not  decompose  when  hermetically  sealed 
and  subjected  to  a  temperature  of  120°  F.  for  one  week. 

It  should  preferably  be  non-hygroscopic,  and  its  facility  for 
detonation  must  not  be  affected  by  moisture  that  can  be  absorbed 
under  ordinary  atmospheric  exposure  necessary  in  handling. 

It  must  not  deteriorate  or  undergo  chemical  change  in  storage. 

GENERAL  CONDITIONS. — Loading  must  not  be  attended  with 
unusual  danger  and  should  not  require  exceptional  skill  or  tedious 
methods. 


EXPLOSIVES.  143 

The  explosive  should  be  obtainable  quickly  in  large  quantities 
and  at  reasonable  cost. 

REMARKS. — The  explosives  used  as  shell  fillers  are  more  stable 
under  severe  heat  treatment  than  the  service  smokeless  powders. 
The  explosives  should  therefore  be  correspondingly  safer  to  store 
in  large  quantities. 

Explosive  D,  used  in  our  service,  invented  by  Major  Beverly  W. 
Dunn,  Ordnance  Department,  is  safer  to  handle  than  black  powder. 

70.  Exploders. — Fulminate  of  mercury  is  one  of  the  most 
violent  explosives.  By  reason  of  its  sensitiveness  to  explosion 
by  heat  or  percussion,  and  the  intensity  of  the  shock  obtained  by 
its  explosion  in  small  quantities,  the  fulminate  of  mercury  is  the 
most  suitable  substance  for  use  in  initiating  detona- 
tions or  explosions  in  other  explosives. 

It  forms  the  principal  or  the  only  ingredient  of  the 
detonating  composition  in  explosive  caps,  primers,  and 
fuses.  Other  ingredients  may  be  potassium  chlorate 
or  nitrate,  or  bisulphide  of  antimony,  the  proportions 
differing  in  order  to  produce  the  best  results  from  the 
particular  explosive  with  which  the  exploder  is  to  be 
used. 

DETONATORS. — A  commercial  detonating  cap  or  fuse 
is  shown  in  the  accompanying  figure.  The  fulminate  of 
mercury,  or  detonating  composition,  B,  is  enclosed  in  a 
copper  case  closed  with  a  plug  of  sulphur  through  which 
pass  the  bared  ends  of  the  electric  wires.  A  platinum 
bridge  connects  the  ends  of  the  wires,  and  the  heating 
of  the  bridge  by  the  electric  current  fires  the  detonator. 

In  order  to  secure  the  best  results  it  is  necessary 
that  the  detonator  be  in  intimate  contact  with  the 
explosive.  It  is  therefore  usually  placed  in  the  midst 
of  the  mass,  and  the  explosive  is  packed  closely 
around  it. 

PRIMERS  FOR  GUNPOWDERS. — For   the  ignition  of 
charges  of  gunpowder  a  large  body  of  flame  is  of  more  advantage 
than   an   intense   shock.       Consequently   in  small-arm  primers 
mercury  fulminate  has  been  replaced  by  a  less  violent  composition 
of  chlorate  of  potash  and  bisulphide  of  antimony,  which  produces 


144  ORDNANCE  AND  GUNNERY. 

a  larger  body  of  flame  and  is  at  the  same  time  less  sensitive  to 
percussion  and  therefore  safer  for  use  in  a  small-arm  cartridge. 
In  primers  for  cannon  the  large  body  of  flame  is  produced  by 
the  use  of  black  powder  for  the  priming  charge  in  the  primer, 
the  ignition  of  the  black  powder  being  effected  by  the  explosion 
of  a  small  percussion  cap  or  by  the  electric  ignition  of  a  small 
quantity  of  loose  guncotton. 

Explosion  by  Influence. — The  detonation  of  a  mass  of  ex- 
plosive may  under  certain  circumstances  induce  the  explosion  of 
another  mass  of  the  same  or  of  a  different  explosive  not  in  contact 
with  the  first.  The  induced  explosion  is  called  an  explosion  by 
influence  or  a  sympathetic  explosion. 

The  ability  of  one  explosive  to  induce  the  sympathetic  explo- 
sion of  another  not  in  contact  with  it  appears  to  depend  on  the 
character  of  the  shock  communicated  by  the  first  explosive.  Abel 
found  that  while  the  detonation  of  guncotton  would  cause  the 
sympathetic  detonation  of  nitroglycerine  in  close  proximity  to  it, 
the  detonation  of  nitroglycerine  would  not  cause  the  detonation 
of  guncotton,  although  nitroglycerine  is  more  powerful  than  gun- 
cotton. 

In  explanation  of  this  difference  in  action  Abel  advanced  the 
theory  of  synchronous  vibrations.  It  is  a  well  established  fact  that 
certain  vibrations  will  induce  the  decomposition  of  chemical  com- 
pounds whose  atoms  are  in  a  state  of  unstable  equilibrium;  and 
according  to  Abel  sympathetic  explosion  is  produced  when  the 
first  explosive  sets  up  in  the  connecting  medium  vibrations  that 
are  synchronous  with  those  that  would  result  from  the  explosion  of 
the  second  explosive. 

This  theory  is  questioned  by  later  investigators,  and  it  is  now 
generally  held  that  sympathetic  explosion  is  due  to  the  trans- 
mission of  a  shock  of  sufficient  intensity. 


EXPLOSIVES.  145 

THEORETICAL  DETERMINATIONS  OF  THE 
RESULTS   FROM   EXPLOSIONS. 

71.  In  the  theoretical  determinations  of  the  results  from  explo- 
sions metric  units  and  the  centigrade  thermometric  scale  are 
usually  employed. 

Definitions.  CALORIE. — A  small  calorie  is  the  quantity  of  heat 
required  to  raise  the  temperature  of  1  gram  of  water  (1  cubic  centi- 
meter) from  0  degrees  to  1  degree  centigrade. 

A  large  calorie  is  the  quantity  of  heat  required  to  raise  the 
temperature  of  1  kilogram  of  water  (1  liter,  1  cubic  decimeter) 
from  0  degrees  to  1  degree.  A  large  calorie  is  equal  to  1000  small 
calories. 

EXOTHERMIC  AND  ENDOTHERMIC  REACTIONS.— An  exother- 
mic reaction  gives  off  heat,  an  endothermic  reaction  absorbs 
heat. 

MOLUGRAM. — The  term  rnolugram  is  used  to  designate  a 
weight  of  as  many  grams  as  there  are  units  in  the  molecular  weight 
of  the  substance.  Thus,  the  molugram  of  hydrogen,  H2,  is  2  grams. 
Water  or  water  vapor,  H20,  has  a  molecular  weight  of  18.  The 
molugram  of  water  is  therefore  18  grams.  The  molugram  of  nitro- 
glycerine, C3H5(N02)303,  is  227  grams. 

The  molugram  of  a  mixture  has  a  weight  in  grams  equal  to  the 
sum  of  the  molecular  weights  of  as  many  molecules  of  each  con- 
stituent as  appear  in  the  formula  for  the  mixture.  Thus,  the 
molugram  of  10KNO3  +  3S+C  is  1119  grams. 

Specific  Heats  of  Gases. — The  specific  heat  of  a  gas  at  constant 
pressure  is  the  number  of  calories  required  to  heat  1  gram  of  the 
gas  from  0°  to  1°  while  the  gas  is  permitted  to  expand  under  the 
constant  pressure. 

The  specific  heat  of  a  gas  at  constant  volume  is  the  number  of 
calories  required  to  heat  1  gram  of  the  gas  from  0°  to  1°,  the  volume 
of  the  gas  remaining  unchanged. 

When  large  calories  are  used  the  unit  weight  of  gas  is  1  kilo- 
gram. 

MOLECULAR  HEAT. — The  molecular  specific  heat  of  a  gas,  or 
more  simply  the  molecular  heat,  is  the  number  of  calories  required 
to  heat  a  molugram  of  the  gas  from  0°  to  1°. 


146  ORDNANCE  AND  GUNNERY. 

The  molecular  heat  is  obtained  by  multiplying  the  specific  heat 
of  the  gas  by  its  molecular  weight.  The  molecular  heat  may  be 
under  constant  pressure  or  under  constant  volume,  depending  upon 
whether  the  specific  heat  used  as  a  multiplier  is  the  specific  heat 
at  constant  pressure  or  at  constant  volume. 

Thus,  carbon  dioxide,  C02;  molecular  weight,  44. 

At  constant  pressure,  specific  heat,  0.2169;  molecular  heat, 
0.2169X44  =  9.5436. 

At  constant  volume,  specific  heat,  0.172;  molecular  heat, 
0.172X44  =  7.568. 

72.  Specific  Volumes  of  Gases. — The  specific  volume  of  a  gas 
is  the  volume  in  cubic  decimeters  (liters)  of  1  gram  of  the  gas  at 
0°  temperature  and  under  atmospheric  pressure  (barometer,  760 
millimeters;  pressure,  103.33  kilograms  per  square  decimeter). 

MOLECULAR  VOLUME. — The  molecular  volume  is  the  volume,  at 
0°  and  760  mm.  pressure,  of  a  molugram  of  the  gas.  It  is  obtained 
by  multiplying  the  specific  volume  by  the  molecular  weight. 

Thus,  CC>2,  specific  volume,  0.5073,  molecular  volume,  44  X 
0.5073  =  22.32  cubic  decimeters  or  liters. 

The  molecular  volumes  of  all  gases  are  the  same,  22.32  liters, 
as  will  be  shown. 

LAW  OF  AVOGADRO. — All  gases  under  the  same  conditions  of 
pressure  and  temperature  haw  the  same  number  of  molecules  in 
equal  volumes. 

It  follows  from  this  law  that  the  single  molecules  of  all  gases, 
whether  simple  or  compound,  occupy  equal  volumes  under  the 
same  conditions  of  pressure  and  temperature. 

The  volume  of  the  hydrogen  atom  is  taken  as  the  unit  volume. 
The  molecule  of  hydiogen  and  the  molecules  of  the  other  simple 
gases  as  well  are  composed  of  two  atoms.  A  molecule  of  any  gas 
therefore  occupies  2  unit  volumes. 

In  the  following  reaction  the  number  of  volumes  appears  under 
each  of  the  symbols 

N  +  H3  =  NH3 

1  vol       3  vols  2  vols. 

That  is,  1  volume  of  N  combining  with  3  volumes  of  H  forms  2 
volumes  of  ammonia,  NH3.  The  volumes  may  be  expressed  in 
any  unit,  as  liters  or  cubic  feet. 


EXPLOSIVES.  147 

The  atomic  weight  of  nitrogen  is  14  and  of  hydrogen  1.  There 
are  therefore  in  the  molecule  of  NH3  17  parts  by  weight  occupying 
the  same  volume  as  2  parts  of  hydrogen  alone.  The  specific  volume 
of  NH3,  the  volume  of  unit  weight,  is  therefore  1/17  of  the  molec- 
ular volume  of  hydrogen,  and  the  molecular  volume  of  NH3, 
which  is  the  specific  volume  multiplied  by  the  molecular  weight,  17 
in  this  case,  is  the  molecular  volume  of  hydrogen. 

As  the  same  is  true  for  any  other  gaseous  compound,  it  follows 
that  the  product  of  the  specific  volume  of  a  gas  by  its  molecular 
weight  is  a  constant  and  is  equal  to  the  molecular  volume  of 
hydrogen. 

The  molecular  volume  of  all  gases  is  22.32  liters. 

By  means  of  the  molecular  volume  we  may  determine  the 
volume  of  any  weight  of  gas,  or  the  weight  of  any  volume, 
since  we  know  that  a  molugram  of  any  gas  occupies  22.32 
liters. 

The  specific  volume,  the  number  of  liters  occupied  by  1  gram, 
is  equal  to  22.32  divided  by  the  molecular  weight. 

The  specific  weight,  the  number  of  grams  occupying  one  liter, 
is  the  reciprocal  of  the  specific  volume,  or  the  molecular  weight 
divided  by  22.32. 

Classification  of  Gases. — Compound  gases  such  as  C02,  NH3, 
C2H4,  whose  molecules  contain  more  than  two  atoms,  are  called 
gases  with  condensation,  as  in  their  formation  more  than  two  atoms 
are  condensed  into  the  volume  of  two  simple  atoms.  Compound 
gases  such  as  CO,  HC1,  whose  molecules  contain  two  atoms,  are 
called  gases  without  condensation.  Oxygen,  hydrogen,  and  nitrogen 
are  simple  or  perfect  gases. 

In  the  following  determinations  of  the  effects  of  explosion  we 
will  follow  the  methods  described  by  Leon  Gody  in  his  work  en- 
titled Matieres  Explosives. 

73.  Quantity  of  Heat. — The  heat  given  off  in  explosions  can 
be  measured  experimentally  by  means  of  special  calorimeters. 
Roux  and  Sarrau  made  use  of  a  very  strong  cylindrical  bomb, 
similar  to  the  apparatus  of  Noble  and  Abel,  illustrated  on  page  67. 
The  bomb,  charged  with  a  few  grams  of  explosive,  was  immersed 
in  a  known  volume  of  water.  After  the  explosion  of  the  charge, 


148  ORDNANCE  AND  GUNNERY. 

effected  electrically,  the  increased  temperature  of  the  body  of 
water  was  noted  and  the  quantity  of  heat  necessary  to  produce 
the  rise  in  temperature  calculated. 

The  theoretical  determination  of  the  quantity  of  heat  resulting 
from  an  explosion  involves  the  application  of  certain  principles  of 
thermochemistry  established  by  Berthelot. 

PRINCIPLE  OF  THE  INITIAL  AND  FINAL  STATE. — The  heat  liber- 
ated (or  absorbed)  in  any  modification  of  a  system  of  simple  or 
compound  bodies,  effected  under  constant  pressure  or  at  constant 
volume  and  without  any  external  mechanical  effect,  depends  solely 
on  the  initial  and  final  states  of  the  system.  It  is  completely  inde- 
pendent of  the  series  of  intermediate  transformations. 

From  this  principle  it  follows  that  the  heat  liberated  in  any 
transformation  accomplished  through  successive  reactions  is  the 
algebraic  sum  of  the  heats  liberated  in  the  different  reactions. 

We  may  consider  the  formation  of  an  explosive  as  an  interme- 
diate reaction  in  the  formation  of  the  products  of  explosion  from 
simple  elements.  If  we  then  subtract  from  the  total  heat  of 
formation  of  the  products  of  explosion  the  heat  of  formation  of  the 
explosive,  the  difference  will  be  the  heat  liberated  in  the  reaction 
of  explosion. 

PRINCIPLE  OF  MAXIMUM  HEAT. — All  chemical  changes  effected 
without  the  intervention  of  external  energy  tend  toward  the  forma- 
tion of  the  body  or  the  system  of  bodies  that  liberates  the  most 
heat. 

The  quantity  of  heat  liberated  or  absorbed  in  a  reaction  is  inde- 
pendent of  the  time  occupied  in  the  reaction. 

74.  Heats  of  Formation. — The  heats  of  formation  at  constant 
pressure  of  the  principal  explosives  and  of  the  gases  resulting  from 
explosion  are  given  in  Table  II  at  the  end  of  the  volume.  The 
heats  are  given  in  large  calories  for  the  molugram  of  each  substance. 
Thus  hydrochloric  acid  gives  off  in  its  formation  22  large  calories; 
that  is,  1  gram  of  hydrogen  and  35.5  grams  of  chlorine  in  com- 
bining give  off  sufficient  heat  to  raise  the  temperature  of  22  kilo- 
grams of  water  from  0°  to  1°.  The  heat  of  formation  of  36.5 
grams  of  HC1  is  therefore  22  large  calories. 

The  heats  of  formation  of  endothermic  bodies  are  preceded  by 
the  minus  sign  in  the  table. 


EXPLOSIVES.  149 

The  atomic  and  molecular  weights  in  Tables  II,  III,  and  IV 
are  those  that  were  in  use  at  the  time  these  tables  were  formed. 
Atomic  weights  according  to  the  latest  determinations  are  given 
in  Table  V.  In  the  examples  which  follow,  involving  the  use  of 
Tables  II,  III,  and  IV,  the  atomic  and  molecular  weights  as  given 
in  those  tables  are  used. 

Quantity  of  Heat  at  Constant  Pressure.  —  In  order  to  determine 
the  quantity  of  heat  given  off  in  any  chemical  change  the  chemical 
reaction  must  be  known.  The  composition  of  explosives  is  gen- 
erally known  and  the  products  of  explosion  can  be  predicted, 
under  the  principle  of  maximum  heat,  when  the  body  undergoes 
complete  combustion;  that  is,  when  it  contains  sufficient  oxygen 
to  form  stable  compounds  of  the  maximum  oxidation. 

The  sum  of  the  heats  of  formation  of  the  products  of  explosion 
that  appear  in  the  formula  for  the  reaction,  minus  the  heat  of 
formation  of  the  explosive,  is  the  quantity  of  heat  liberated  by  the 
explosion. 

Example  i.  —  As  an  example  we  will  find  the  heat  given  off  in 
the  explosion  of  nitroglycerine  under  constant  pressure,  as  in  the 
open  air. 

The  equation  of  the  reaction  is  as  follows  : 


454  264  90  84          16 

i 

With  the  heats  of  formation  from  Table  II  for  the  molugram 
of  each  substance  we  obtain,  for  the  numbers  of  molecules  in  the 
reaction, 

2C3H5(NO2)303,  2X98    =196, 

6CO2,  6X94.3  =  565.8, 

5H20,  5X58.2  =  291. 

The  nitrogen  and  oxygen  being  simple  elements  add  no  heat. 

We  therefore  have  for  the  heat  given  off  by  the  explosion  under 
constant  pressure  of  2X227  grams  of  nitroglycerine 

(565.8+291)-196  =  660.8  1.  cal.,*  _ 

*  In  other  works  the  abbreviation  used  to  designate  a  large  calorie  is  cal.  k.  d. 
(kilogram-degree),  and  for  a  small  calorie,  cal.  g.  d.  (gram-degree).  The  ab- 
breviations I.  cal.  and  s.  cal.  are  used  here,  as  they  more  plainly  indicate  the 
words  abbreviated. 


150  ORDNANCE  AND  GUNNERY. 

and  for  the  heat  given  off  by  227  grams  of  the  explosive,  a  molu- 
gram, 

Qmp  =  660.8/2  =  330.4  1.  cal. 

For  the  heat  given  off  by  a  kilogram  of  the  explosive, 
330.4X1000 


227 


=     55'5   '  Cal> 


75.  When  Solid  Products  are  Formed.  —  If  the  explosion 
produces  solid  products  the  heats  of  formation  of  these  bodies 
are  added  to  the  heats  of  formation  of  the  gases  in  the  determina- 
tion of  Qmp  and  Qkp. 

Example  2.  —  A  mixture  of  nitrobenzol  with  sufficient  potas- 
sium chlorate  to  make  the  combustion  of  the  nitrobenzol  com- 
plete is  exploded. 

The  reaction  is 


2C6H5N02  +  -2/KC103  =  12C02  +  5H2O  +  N2  + 

1266.8  528  90          28        620.8 

A.  molugram  of  a  mixture  is  the  sum  of  the  molecular  weights 
in  grams  of  as  many  molecules  of  each  of  the  constituents  as 
appear  in  the  reaction.  The  molugram  of  this  explosive  mixture 
is  therefore  2  X  123  +  \s-  X  122.5  =  1266.8  grams. 

Heats  of  formation  : 

12C02,  12  X  94.3  =  1131.6 

5H20,  5X  58.2=  291 

•V-KC1,  -2/Xl05    =  875 


2297.6 

2C6H5N02,       2X     4.2=       8.4 

94.6=  788.3 


796.7 

=  2297.6-796.7  =  1500.9  1.  cal. 

1500.9X1000    11Q 

=1184-81-cal- 


EXPLOSIVES.  151 

Incomplete  Combustion.  —  When  an  explosive  does  not  con- 
tain sufficient  oxygen  for  complete  combustion  the  products 
formed  vary  with  the  temperature,  the  pressure,  and  the  density 
of  loading.  Therefore  no  fixed  formula  can  be  written  for  the 
reaction.  The  products  of  combustion  of  these  explosives  are 
determined  by  analysis,  and  the  heat  given  off  may  then  be  deter- 
mined as  above. 

The  explosion  of  guncotton  under  atmospheric  pressure  gives 
the  following  reaction. 


ii  =  1500  +  9C02  +  9H20  +  5.5H2  +  5.5N2 
Under  high  pressure  the  reaction  is  as  follows. 
C24H29b20(N02)ii  =  12CO  +  12C02  +  6H20  +  8.5H2  +  5.5N2 

76.  Quantity  of  Heat  at  Constant  Volume.  —  If  the  decom- 
position takes  place  at  constant  volume,  for  instance  in  a  closed 
vessel,  the  heat  developed  is  greater  than  in  the  open  air  under 
constant  pressure.  The  gases  developed  in  the  open  air  perform 
the  work  of  driving  back  the  air,  and  this  work  absorbs  some 
of  the  heat. 

Let  Qmp  be  the  heat  given  off  by  the  molugram  of  the  substance 
in  the  reaction  at  constant  pressure  at  the  surround- 
temperature  t, 

Qmv  the  heat  given  off  by  the  molugram  of  the  substance 
in  the  reaction  at  constant  volume  at  the  surround- 
ing temperature  t, 

W     the  work  of  expansion  at  constant  pressure, 
E      the    mechanical   equivalent    of  heat,   425   kilogram- 

meters. 

Then  W  /E  is  the  heat  expended  in  performing  the  work  of  driving 
back  the  air,  and 

(1) 


But  the  work  W  due  to  the  pressure  of  the  gas  against  the 
constant  pressure  p  is,  as  shown  by  equation  (40),  page  65, 

W  =  /Vlpdv  =  p  I  Vldv 

J  Vb  J  Vb 


152  ORDNANCE  AND  GUNNERY. 

Vb  and  Vi  representing  the  volumes  of  the  gas  before  and  after 
expansion. 

Performing  the  indicated  integration, 

W-p^-Vb)  (2) 

Taking  the  molecular  volume  at  0°  and  760  mm.,  22.32  liters, 
as  the  unit  volume, 

Let  rib  represent  the  number  of  unit  volumes  before  expansion, 
n\  the  number  of  unit  volumes  after  expansion  to  normal 

atmospheric  conditions. 

n\  will  also  represent  the  number  of  gaseous  molecules,  since  after 
expansion  to  the  normal  atmospheric  conditions  of  temperature' 
and  pressure  each  unit  volume  is  occupied  by  a  molecule.  ^ 

Then  from  Gay-Lussac's  law,  page  58,  we  have  at  the  tem- 
perature t 


Substituting  these  values  in  equation  (2)  we  have 


W    v 
Whence  ^r=  ^22.32  (ni-n6)(l+aQ  (3) 

The  value  425  for  E,  the  mechanical  equivalent  of  heat,  is 
expressed  in  kilogrammeters.  We  must  therefore  express  p, 
the  normal  atmospheric  pressure  in  kilograms  per  square  meter, 
103.3x100,  and  the  volume  22.32  liters  (cubic  decimeters)  in 
cubic  meters,  22.32/1000. 

Equation  (3)  then  becomes 

W     10330X22.32. 


425X1000 
or 

«  =  1/273    and     1/273x0.5424  =  0.002,  nearly 
Therefore 


(4) 


EXPLOSIVES.  153 

In  the  case  of  explosives  the  volume  vb  is  generally  negligible 
with  respect  to  v\.  Vb  represents  the  volume  of  the  explosive  for 
those  explosives  that  are  completely  converted  into  gas.  rib  is 
therefore  negligible  with  respect  to  n\,  and  equation  (4)  becomes 

W/E  =  0.5424m  +  0.002rM 
Substituting  this  value  in  equation  (1) 

Qm,  =  Qmp+  0.5424ft!  +  0.002?M 

We  will  make  i  =  15°,  since  the  heats  of  formation  in  Table  II 
have  been  determined  for  that  temperature,  and  Qmp  and  Qmv  in 
the  above  equation  will  be  determined  from  the  table.  We  have, 
then,  finally, 

(5) 


for  the  quantity  of  heat  given  off  at  constant  volume  by  the  molu- 
gram  of  the  explosive. 

77.  Example  3.  —  Take,  for  example,  nitroglycerine, 

2C3H5(NO2)303=6C02+5H20  +  3N2  +  |02 

454  264  90  84         16 

We  have  found  at  constant  pressure,  example  1, 

Qmp  =  330.4  1.  cal. 

From  the  reaction  we  see  that  2  molugr.ams  of  the  explosive  give 
off  6  +  5  +  3  +  0.5  =  14.5  molecular  volumes  of  gas.     1  molugram, 

therefore,  gives 

HI  =  7.25  volumes 

Substituting  in  equation  (5)  we  obtain 

Qmv  =  330.4  +  0.5724  X  7.25  =  334.5  1.  cal. 
For  1  kilogram  of  the  explosive,  example  1, 


-X  1000  -1473.6  Leal 


We  found  at  constant  pressure 

Qkp  =  1455.5  1.  cal. 


154  ORDNANCE  AND  GUNNERY. 

Potential.  —  The  potential  has  been  denned  as  the  total  work 
that  can  be  performed  by  the  gas  from  unit  weight  of  the  explosive 
under  indefinite  adiabatic  expansion.  The  kilogram  is  taken  as 
the  unit  weight  in  the  determination  of  the  potential,  and  the 
meter  as  the  unit  of  length.  The  work  unit  is  therefore  the  kilo- 
gramineter.  The  total  work  from  one  kilogram  of  the  explosive 
is  equal  to  the  maximum  quantity  of  heat  given  off  by  one  kilo- 
gram multiplied  by  the  mechanical  equivalent  of  heat. 

The  mechanical  equivalent  of  heat  is  425  kilogrammeters. 
Therefore  representing  the  potential,  the  total  work  from  a  kilo- 
gram of  the  explosive,  by  Wk  we  have 

Wk  =  QKV  X  425  kilogrammeters  (6) 

78.  Volume  of  Gases.  —  The  volume  of  gases  produced  by  ex- 
plosion may  be  measured  experimentally,  the  gases  being  drawn 
off  from  the  calorimetric  bomb  for  this  purpose. 

The  volume  of  the  gases  may  also  be  determined  theoretically 
from  the  reaction. 

As  previously  explained,  the  molecular  volume  (the  volume  of 
the  molugram)  of  any  gas,  simple  or  compound,  is  22.32  liters. 
Therefore  in  any  reaction  the  molecular  volume,  at  standard  tem- 
perature and  pressure,  of  the  evolved  gases  is  very  simply  obtained 
by  multiplying  the  number  of  gaseous  molecules  in  the  formula 
for  the  reaction  by  22.32. 

Example  4.  —  A  formula  for  the  explosion  of  black  gunpowder 
is 

lOKNOs  +  3S  +  8C  =  3K2SO4  +  2K2CO3  +  6C02  +  5N2 

1010     96   96     522      276      264    140 

The  first  two  products  of  the  reaction  are  solid.  The  gaseous  prod- 
ucts are  6  molecules  of  CO2  and  5  of  N.  Therefore  the  molecular 
volume  of  the  gases  from  1202  grains  of  the  explosive  is,  at  0°  and 
760mm., 

Vm=  11X22.32  =  245.52  liters 


and  from  1  kilogram  of  explosive 
245.52X1000 


=  204.26  liters 


EXPLOSIVES.  155 

The  volumes  at  any  other  pressure  or  temperature  may  be  ob- 
tained by  means  of  equations  (31)  and  (34),  Chapter  III. 

79.  Temperature  of  Explosion. — The  method  of  Mallard  and 
Le  Chatelier  for  calculating  the  temperature  of  explosion  at  con- 
stant volume  in  a  closed  vessel  is  as  follows. 

The  quantity  of  heat  liberated  by  the  explosion  of  the  molu- 
gram  of  the  explosive  would,  if  the  specific  heat  of  the  products 
were  constant,  be  equal  to  the  molecular  specific  heat  multiplied 
by  the  rise  in  temperature.  We  would  then  have 

Qmv  =  Cmv  X  t\  (7) 

from  which  ti,  the  rise  in  temperature,  could  be  obtained.  Assum- 
ing 15°,  an  ordinary  temperature,  as  the  temperature  of  the  ex- 
plosive when  fired,  the  temperature  of  explosion  would  then  be 

t  =  ti  +  15  (8) 

But  it  is  known  that  the  specific  heat  increases  with  the  tem- 
perature. Assuming  that  the  specific  heat  varies  with  the  tem- 
perature in  the  manner  represented  by  the  linear  expression, 

Cmv  =  a+bk  (9) 

the  values  of  a  and  6,  and  the  consequent  values  of  Cmv,  have 
been  deduced  for  certain  gases  as  follows.  The  values  are  given  in 
small  calories. 

a  b 

For  CO2,  SO2,        6.26     0.0037         Cmv  =  6.26  +  0.0037  k 

For  H20,  5.61     0.0033         Gm,  =  5.61  +  0.0033  ti 

For  gases  without 
condensation,     4.80     0.0006         <?«. =4.80+0. 0006  k 

The  values  of  a  are  the  molecular  heats  of  the  gases  in  small 
calories  at  the  temperature  15°,  and  the  values  of  b  are  the  incre- 
ments of  the  molecular  heats  for  each  degree  of  rise  in  temperature. 

Suppose  that  the  products  of  an  explosion  are  as  follows: 


156  ORDNANCE  AND  GUNNERY. 

P  representing  a  molecule  of  a  perfect  gas.     The  coefficients  a 
and  b  for  the  products  of  explosion  will  then  be 

a  =  6.26  a  +  5.61  /?+4.8  d  (10) 

6  =  0.0037  a  +  0.0033/3+  0.0006  d  (11) 

Combining  equations  (7)  and  (9)  and  multiplying  Qmv  by  1000, 
since  it  has  been  determined  in  large  calories,  and  a  and  b  are  now 
in  small  calories,  we  obtain 


Solving  this  equation  for   t\   and  substituting   the  resulting 
value  in  equation  (8),  we  obtain,  for  the  temperature  of  explosion 


t=        '         2&  ""'  +  15  (12) 

80.  Example  5.  —  Nitroglycerine.     Qmt  =  334.5  1.  cal.  (see  ex- 
ample 3). 


03  =  6C02  +  5H20  +  3N2  +  0.502 

454  264  90  84  16 

Since  the  products,  as  given  in  the  formula,  are  from  two  molecules 
of  the  explosive, 


26  =  0.0037  X  6  +  0.0033  X  5  +  0.0006  X  (3  +  0.5)  =  0.0408 
a  =  41. 205  6  =  0.0204 

and  from  equation  (12) 

-  41 .205  +  \/4L2052  +  4000  X  0.0204  X  334.5 
2X0.0204 

81.  Temperature  when  Solid  Products  are  Formed.— If  the 

explosion  gives  rise  to  solid  products  the  heat  absorbed  in  raising 
the  temperature  of  these  products  must  be  considered.     In  equa- 


EXPLOSIVES.  157 

tion  (7)  Cmv  must  be  the  mean  specific  heat  of  the  products  of 
the  explosion  of  a  molugram  of  the  explosive. 

Suppose  that  in  addition  to  the  gaseous  products  assumed 
above,  page  155,  we  have  x  molugrams  of  a  solid  product  having 
a  specific  heat  h  referred  to  its  molecular  weight.  Then  a,  equa- 
tion (10),  becomes 

a  =  6.26a  +  5.61/?+4.8<H/iz  (13) 

The  specific  heat  of  a  solid  product  is  assumed  not  to  vary 
with  the  temperature,  therefore  the  value  of  b  as  given  by  equa- 
tion (11)  is  not  affected. 

The  specific  heats  of  substances  will  be  found  in  Table  III  at 
the  end  of  the  volume. 

Example  6.  —  Determine  the  temperature  of  explosion  of  the 
mixture  of  nitrobenzol  and  potassium  chlorate  of  example  2. 

The  reaction  is 


2C6H5N02  +  ¥KC1O3  =  12C02  +  5H2O  +  N2  + 

1266.8  528  90          28         620.8 

From  example  2,  Qmp  =  1500.9  1.  cal. 

equation  (5),        Qmv  =Qmp+  0.5724% 
page  152,  ni  =  12  +  5  +  l  =  18 

Qmv  =  1511.2 

From  Table  III,  molecular  specific  heat  of  KC1,  12.89 
eq.  (13),   a  =  6.26X!2  +  5.6lX5  +  4.8+12.89x25/3  = 
eq.  (11),   6=0.0037X12  +  0.0033X5  +  0.0006=0.0615 


-  215.39  +v/215.392  +  4000  X  0.0615  X  1511.2 
t=  2X0.0615 

£  =  3521°. 

82.  Pressure  in  a  Closed  Chamber.  —  The  pressure  of  the  gases 
produced  by  explosion  is  a  function  of  the  volume  occupied  by 
the  gases.  In  a  closed  chamber  the  volume  available  for  the  gases 
depends  upon  whether  the  products  of  explosion  are  wholly  gaseous 
or  whether  they  contain  non-gaseous  matter  as  well. 


158  ORDNANCE  AND  GUNNERY. 

PRODUCTS  WHOLLY  GASEOUS.  —  We  have  deduced  inequation 
(47),  Chapter  III,  the  following  value  for  the  force  of  an  explosive. 

f  =  p0v0T/273  (14) 

in  which,  in  the  metric  units  that  have  been  chiefly  used  in  the 
previous  calculations,  the  kilogram  and  the  decimeter, 

/  is  the  pressure  per  square  decimeter  of  the  gases  from  1  kilo- 
gram of  explosive,  the  gases  occupying  at  the  tempera- 
ture of  explosion  a  volume  of  1  cubic  decimeter. 
PO  the  normal  atmospheric  pressure,  103.3  kilograms  per  square 

decimeter, 

VQ  the  specific  volume  of  the  gas,  now  taken  as  the  volume  in 
cubic  decimeters  occupied  by  1  kilogram  of  the  gas  at  0° 
and  760  mm., 

T  the  absolute  temperature. 

The  volume  Vk,  as  determined  on  page  154,  is  the  volume  in 
cubic  decimeters,  or  liters,  of  the  gaseous  products  from  1  kilogram 
of  the  explosive.  Therefore 

v0  =  Vk  (15) 

The  absolute  temperature  T  =  273  +  t,  in  which  t,  the  tempera- 
ture of  explosion,  is  taken  as  the  rise  in  temperature  due  to  the 
explosion  plus  15°,  which  is  the  assumed  temperature  of  the 
explosive  when  fired. 

Substituting  the  values  of  p0,  v0,  and  T  in  equation  (14)  we 
obtain  for  the  force  of  the  powder 

103.37»(273  +  Q  .  .. 
/=  -  270  -      kilograms  per  sq.  dec.  (16) 

RELATION  BETWEEN  PRESSURE,  FORCE  OF  EXPLOSIVE,  AND 
DENSITY  OF  LOADING.  —  We  have,  equation  (49),  Chapter  III,  for 
the  pressure  from  unit  weight  of  gas  confined  in  the  volume  v, 

(17) 


v—  a 
in  which  a  is  the  covolume  of  the  gas. 


EXPLOSIVES.  159 

By  the  process  followed  in  Chapter  III  in  deducing  equation 
(46)  from  equation  (45)  this  equation  may  be  put  in  the  form 

P  =  T~  (18)* 

1  —  aA 

in  which  P  is  the  pressure  per  unit  of  surface  of  the  gases  from 

CD  units  of  weight  of  explosive, 
A  is  the  density  of  loading. 

According  to  Sarrau  the  covolume  is  1/1000  of  the  specific 
volume  of  the  gases.  Therefore  when  the  products  are  wholly 
gaseous  we  have  from  equation  (15) 

a  =  Ffc/1000  (19) 

83.  Non-gaseous  Products. — When  solid  or  liquid  products 
result  from  the  explosion,  these  products  occupy  part  of  the 
volume  in  the  chamber  and  diminish  the  volume  occupied  by  the 
gases. 

Let  y  be  the  weight  of  gas  from  unit  weight  of  explosive, 
MO  the  volume  at  0°  and  760  mm.,  occupied  by  the  gas  from 

unit  weight  of  explosive, 

a'  the  volume,  at  temperature  and  pressure  of  explosion,  of 
the  non-gaseous  residue  from  unit  weight  of  explosive. 
In  this  case  if  we  consider  as  the  specific  volume  of  the  gas 
the  volume  WQ  occupied  by  the  gas  from  unit  weight  of  the  ex- 
plosive instead  of  the  volume  VQ  occupied  by  unit  weight  of  the 
gas,  /,  equation  (14),  becomes  for  the  new  specific  volume 

f  =  p0w0T/273  (20) 

And  if  we  consider  that  a,  the  subtractive  term  in  equation  (14), 
includes  the  volume  of  the  residue  from  unit  weight  of  explosive 
as  well  as  the  covolume  of  the  gases  for  the  new  specific  volume, 

a  =  a'  +  wo/1000  (21) 

*  This  equation  is  identical  with  equation  (46),  Chapter  III,  deduced  by 
Noble  and  Abel.  They  considered  a  as  the  volume  of  the  solid  residue  from 
unit  weight  of  powder,  but  later  investigations  show,  as  explained  in  Chapter 
III,  that  the  covolume  of  the  gases  must  appear  in  the  equation.  When  solid 
products  result  the  value  of  a  must  be  modified  to  include  the  volume  occupied 
by  the  solid  products. 


160  ORDNANCE  AND  GUNNERY. 

By  definition  we  have 

wQ  =  v0y  (22) 

With  these  new  values  of  /  and  a  equation  (17)  gives  the 
pressure  due  to  the  gases  from  unit  weight  of  the  explosive,  and 
equation  (18)  may  be  deduced  from  it  as  before. 

Therefore  when  non-gaseous  products  result  from  the  ex- 
plosion the  pressure  is  obtained  from  equation  (18)  by  substituting 
for  /  and  a  the  values  given  in  equations  (20)  and  (21). 

The  volume  of  the  solid  matter  is  easy  to  calculate,  as  from 
the  formula  of  the  decomposition  we  may  obtain  the  weight  of  the 
residue  from  1  kilogram  of  the  explosive,  and  it  is  only  necessary 
to  divide  this  weight  by  the  density. 

The  densities  of  substances  are  given  in  Table  IV  at  the  end 
of  the  volume. 

84.  Example  7.  —  What  is  the  pressure  in  a  closed  chamber 
of  a  charge  of  the  explosive  of  example  6,  the  density  of  loading 
being  0.9? 

The  reaction  is 


2C6H5NO2  +  ^KC103  =  12C02  +  5H20  +  N2 

1266.8  528  90         28         620.8 

From  example  6,     Qmp  =  1500.9 
mv  =  1511.2 


Following  example  4, 

Ffc  =  18x22.32xlOOO/1266.8  =  317.15  =  i>o>  equation  (15) 


KCl.  Gas. 

1266.8  kilos  explosive  produce,  kilos  ......  620.8  646 

1  kilo  explosive  produces,  kilos  ...........  0.49  0.51  =y 

Divide  by  density  KCl,  1.94,  Table  IV  ____  0.2526  =  a' 

Eq.  (22),    WQ  =  317.15X0.51  -161.75 
Eq.  (21),      a  =  0.2526x0.  161  7  =  0.0408 


EXPLOSIVES.  161 

Eq.  (20) ,       /  =  103.3  X 161 .75  X  3794/273  =  232210  kilos  per  sq.  dec. 

232210x0  9 
Eq.  (18),      P^1_  (004Q8 XQ9)=  216960  kilos  per  sq.  dec. 

For  A  =  1,  P  =  242090  kilos  per  sq.  dec. 

SPECIFIC  HEATS  AND  DENSITIES  OF  NON-GASEOUS  PRODUCTS. — 
It  is  assumed  in  the  above  discussion  that  the  specific  heats  and 
densities  of  the  non-gaseous  products  remain  constant.  This 
assumption  is  generally  inaccurate,  and  the  calculated  values  of 
force  and  pressure  for  explosives  that  yield  non-gaseous  products 
are  therefore  uncertain.  For  these  explosives  the  most  satis- 
factory determinations  are  made  by  experiment.  Two  or  more 
charges  of  the  explosive  are  exploded  in  a  closed  chamber  and 
the  values  of  P  measured.  Substituting  these  with  the  corre- 
sponding known  values  of  J  in  equation  (18)  the  values  of  /  and 
a  are  determined. 

85  Complete  Calculation  of  the  Effects  of  Explosion.— 
The  formula  of  the  reaction  for  the  complete  combustion  of 
Sprengel's  explosive  acid,  a  mixture  of  picric  acid  and  nitric  acid, 
is  as  follows. 

5C6H2  (N02)3OH  +  13HN03  =  30C02  +  14H2O  +  14N2 

1145  819  1320  252  392 

The  molecular  weight  is  1145  +  819  =  1964. 

In  the  work  that  follows,  the  number  of  the  page  on  which  the 
process  is  explained,  or  the  number  of  the  equation  from  which 
the  value  is  derived,  appears  on  the  left. 

146,  QmP  =  (30X94.3  +  14X58.2)-  (5X49.1  +  13X41.6) 
=  2857.5  1.  cal. 

150,  Qkp  =  2857.5X^  =  1454.9  Leal. 

(5)  Qw,  =  2857.5+0.5724(30  +  14  +  14)  =2890.71.  cal. 
153,    Qkv  =  2890.7  X  ^5  =  1471 .8  1.  cal. 

(6)  Wk  =  1471 .8  X  425  =  625515  kgm. 


162  ORDNANCE  AND  GUNNERY. 


154,    Vm  =  (30+14+14)22.32  =  1294.56  liters 

1000 
154,     Vk  =  1294.56  X         =  659.14  liters 


(10)  a  =  6.26X30  +5.61X14  +  4.8X14  =  333.54 

(11)  6  =  0.0037X30  +  0.0033X14+0.0006X14=0.1656 


-  333.54  +  ^333.542  +  4000  X  0.1656  X  2890.7 
(12)  2X0.1656  -  +  15 

=  3306° 

103.3  X  659.14(273  +  3306) 
(16)       /  =  -  ~  =  89265°  k8m-  Per  S(l-  dec 


(19) 


892650J 
^    ^  -  ^HSrams  per  sq.  dec. 


1-  0.65914  J 
For        A  =  0.8,        P  =  1510700  kilograms  per  sq.  dec. 


CHAPTER  V. 
METALS  USED  IN  ORDNANCE  CONSTRUCTION. 

86.  Stress  and  Strain. — A  proper  understanding  of  these  terms 
will  be  helpful  in  what  follows. 

When  a  force  is  applied  to  a  body  the  effect  produced  depends 
upon  whether  or  not  the  body  is  free  to  move.  A  force  applied 
to  a  free  body  produces  motion  of  the  body.  A  force  applied  to  a 
fixed  body  produces  change  of  form  of  the  body. 

Stress  is  the  name  given  to  any  force  or  part  of  a  force  that 
produces  change  of  form  of  the  body.  The  component  forces  or 
pressures  induced  in  the  interior  of  the  body  are  also  called  stresses. 

Strain  is  the  effect  of  the  force  as  measured  by  the  change  in 
form  of  the  body  to  which  the  stress  is  applied. 

Stresses  are  of  different  kinds,  depending  on  the  manner  of  ap- 
plication of  the  force;  as  tensile  stress,  compressive  stress,  tor- 
sional  stress.  A  torsional  stress  is  a  compound  stress  and  may  be 
resolved  into  a  tensile  stress  on  some  elements  of  the  material  and 
a  compressive  stress  on  others. 

Each  kind  of  stress  produces  a  corresponding  strain,  or  effect 
on  the  material,  the  tensile  stress  producing  elongation,  the  com- 
pressive stress  compression.  As  all  stresses  may  be  resolved  into 
tensile  and  compressive  stresses,  all  strains  may  be  resolved  into 
elongation  and  compression. 

Physical  Qualities  of  Metals. — The  following  qualities  of  metals 
are  those  with  which  we  are  most  concerned  in  ordnance  construc- 
tion. 

Fusibility. — The  property  of  being  readily  converted  into  the 
liquid  form  by  heat. 

Malkability. — The  property  of  being  permanently  extended  in 
all  directions  without  rupture  when  hammered  or  rolled. 

Ductility. — The  property  of  being  permanently  extended  with- 
out rupture  by  a  tensile  stress,  as  in  wire-drawing. 

163 


164  ORDNANCE  AND  GUNNERY.  . 

Hardness. — The  property  of  resisting  change  of  form  under  a 
compressive  stress.  A  hard  metal  offers  great  resistance  to  such 
a  stress,  while  a  soft  metal  yields  readily  and  changes  its  form 
without  rupture.  The  terms  hardness  and  softness  are  of  course 
comparative  only. 

Toughness. — The  property  of  resisting  fracture  under  change  of 
form  produced  by  any  stress. 

Elasticity. — The  property  of  resisting  permanent  deformation 
under  change  of  form.  This  is  one  of  the  most  important  proper- 
ties of  gun  metals,  which  under  the  high  stresses  due  to  the  ex- 
plosion are  subjected  to  extensive  deformation.  Through  this 
property  the  deformations  disappear  on  the  cessation  of  the  stress 
and  the  metal  resumes  its  original  dimensions. 

Strength  of  Metals. — The  strength  of  metals  is  ordinarily  de- 
termined by  physical  tests  in  a  testing  machine.  As  the  tensile 
strength  of  metals  is  less  than  the  compressive  strength,  usually  a 
tensile  test  only  is  applied.  A  test  specimen  is  cut  from  the  metal 
to  be  tested  and  is  prepared  in  suitable  form  to  be  inserted  in  the 
machine.  The  area  of  the  cross  section  of  the  test  specimen  is 
usually  a  square  inch  or  some  aliquot  part  of  a  square  inch. 

In  the  machine  the  test  piece  is  subjected  to  a  tensile  stress, 
the  amount  of  which  is  recorded  by  a  sliding  weight  on  a  scaled 
beam.  The  test  piece  stretches  under  the  applied  stress.  With 
elastic  metals  it  will  be  found  that  up  to  the  application  of  a 
certain  stress  the  test  piece  will  resume  its  original  length  if 
the  stress  is  removed,  but  on  the  application  of  a  stress 
greater  than  this  the  test  piece  will  remain  permanently  elongated. 
When  permanent  distortion  occurs  the  metal  is  said  to  have  a 
permanent  set. 

ELASTIC  LIMIT. — The  stress  per  square  inch  applied  at  the 
moment  that  the  permanent  set  occurs  is  called  the  elastic  limit  of 
the  metal.  Within  this  limit  the  metal  has  practically  perfect 
-elasticity  and  does  not  suffer  permanent  deformation. 

As  the  stress  increases  beyond  the  elastic  limit  the  metal  stretches 
permanently  and  more  rapidly,  the  cross  section  at  the  weakest 
point  reduces,  and  finally  the  test  piece  ruptures. 

The  elastic  strength  of  metals  will  be  found  more  fully  treated 
in  the  discussion  of  the  elastic  strength  of  guns  in  Chapter  VI. 


METALS   USED  IN  ORDNANCE  CONSTRUCTION. 


165 


87.  TENSILE  STRENGTH. — The  stress  per  square  inch  that  pro- 
duces rupture  of  the  metal  is  called  the  tensile  strength. 

ELONGATION  AT  RUPTURE  AND  REDUCTION  OF  AREA. — In  ord- 
nance structures  the  stresses  are  not  expected  to  exceed  the  elastic 
limit  of  the  metal,  but  should  they  by  any  chance  exceed  this  limit 
the  tensile  strength  of  the  metal  and  its  capacity  to  permanently 
elongate  before  rupture  become  of  importance.  The  permanent 
elongation  will  serve  as  a  warning  that  the  elastic  strength  has 
been  exceeded.  The  reduction  of  area  of  cross  section  is  intimately 
connected  with  the  elongation.  In  the  tests  of  metals  for  ordnance 
purposes  these  particulars  are  therefore  always  noted  and  limits  are 
prescribed.  For  the  measurement  of  the  elongation  at  rupture  the 
parts  of  the  ruptured  test  piece  are  brought  together  and  the  dis- 
tance is  measured  between  two  punch  marks  that  were  made  on 
the  test  piece  before  insertion  in  the  testing  machine. 

The  tensile  test  therefore  includes  the  determination  of  the 
elastic  limit,  the  tensile  strength,  the  elongation  at  rupture,  and  the 
reduction  of  area  of  cross  section.  The  last  two  are  recorded  in 
percentages  of  the  original  dimensions. 

The  following  table  shows  the  physical  requirements  demanded 
by  the  Ordnance  Department  in  the  principal  metals  used  in  ord- 


Elastic 
Limit. 

Tensile 
Strength  . 

Elongation 
at  Rupture. 

Contraction 
of  Area. 

Copper  

Ibs.  per  sq.  in. 

Ibs.  per  sq.  in. 

32,000 

per  cent. 
22.0 

per  cent. 

Bronze,  No.  1  ,  

28,000 

Bronze,  No   4   

60,000 

20  0 

Tobin  bronze  

60,000 

25.0 

Cast  iron,  No.  1  

22,000 

Cast  iron,  No.  2  

*  28,000 

Wrought  iron  

22000 

50,000 

25.0 

35  0 

Cast  steel,  No   1  

25000 

60,000 

16.0 

24  0 

Cast  steel,  No   3  

45000 

85,000 

12.0 

18  0 

Forged  steel,  No.  1  

27,000 

60,000 

28.0 

40.0 

Forged  steel  (caps)  

f  60,000 

30.0 

45.0 

Forged  steel  (tubes)  

46,000 

86,000 

17.0 

30.0 

Forged  steel  (jackets)  

48,000 

90,000 

16.0 

27.0 

Forged  steel  (hoops)   

53,000 

93000 

14.0 

20.0 

Forged  steel,  D  

100,000 

120,000 

14.0 

30.0 

Nickel  steel  

65,000 

95,000 

18.0 

30.0 

Steel  wire  (guns)  

100,000 

160,000 

*  Cast  iron  No.  2  must  not  show  a  tensile  strength  of  more  than  39,000 
pounds  per  square  inch. 

t  The  tensile  strength  of  steel  used  in  caps  for  armor  piercing  projectiles 
must  not  exceed  60,000  pounds. 


166 


ORDNANCE  AND  GUNNERY. 


nance  construction,   the  requirements  varying  for  each  kind  of 
metal  according  to  the  use  to  which  it  is  destined. 

Testing  Machine. — The  standard  government  testing  machine 
is  at  Watertown  Arsenal,  Mass.  It  has  a  testing  capacity  of 
800,000  Ibs. 

A  smaller  testing  machine,  with  a  capacity  of  50,000  Ibs.,  is 
shown  in  Fig.  26.  The  specimen  of  the  metal  to  be  tested  is  turned 
to  the  shape  shown  by  the  piece  marked  1.  The  ends  of  the  test 
specimen  are  grasped  by  clamps  fixed  in  the  upper  fixed  head,  /, 
of  the  machine  and  in  the  lower  movable  head  m.  Four  heavy 
vertical  screws  pass  through  the  corners  of  the  movable  head,  and 
by  their  means  the  movable  head  is  moved  toward  or  from  the 
fixed  head,  exerting  on  the  specimen  held  between  the  clamps  a 
force  of  compression  or  of  extension  as  desired.  The  amount  of 
this  force  is  measured  by  a  sliding  weight,  w,  on  a  scaled  beam  in 
the  same  manner  as  a  weight  is  determined  on  an  ordinary  scale. 
The  total  force  divided  by  the  area  of  cross  section  of  the  test 
specimen  gives  the  force  exerted  per  square  inch. 

A  graphic  representation  of  the  relation  between  the  force 
exerted  and  the  change  in  length  of  the  test  specimen  is  made  on 
the  indicator  card,  c.  An  indicator  card,  showing  the  results  of 
tensile  tests  on  specimens  of  several  metals,  is  shown  in  Fig.  25. 
Within  the  elastic  limit  of  the  metal  the  elongation  of  the 

test  piece  is  proportional  to 
the  tensile  stress.  Up  to  this 
point,  therefore,  the  line  made 
by  the  indicator  will  be  a  straight 
line.  At  the  elastic  limit,  where 
the  bends  occur  in  Fig.  25,  per- 
manent set  occurs,  and  the  test 
piece  thereafter  elongates  more 
rapidly  than  the  stress  in- 
creases. 

To  prevent  injury  to  the  in- 
dicating apparatus  by  the  shock 
that  occurs  when  the  test  piece 
breaks,  the  indicator  is  usually 
disconnected  after  the  elastic  limit  has  been  registered. 


IBs. 

iuooo 


'10 


0.2         0,3         IU 

FIG.  25. 


o 

1. 

«< 


METALS  USED  IN  ORDNANCE  CONSTRUCTION.  167 

Broken  test-pieces  are  shown  at  2  and  3  in  Fig.  26.  Comparing 
these  with  test  piece  1,  the  effects  of  the  test,  the  elongation  at 
rupture,  and  the  contraction  of  area  are  apparent. 

88.  Copper,  Brass,  Bronze. — Pure  copper  is  used  for  the  bands 
of  projectiles.  In  alloys,  as  brass  and  bronze,  it  enters  into  the 
construction  of  parts  of  guns  and  gun  carriages  not  usually  sub- 
jected to  great  stress.  In  this  form,  too,  it  is  extensively  employed 
in  the  manufacture  of  cartridge  cases,  fuses,  primers,  gun  sights, 
and  instruments.  Brass  is  an  alloy  of  copper  with  zinc.  Bronze 
is  an  alloy  of  copper  with  tin  and  usually  a  small  quantity  of  zinc. 
The  addition  of  zinc  or  tin  produces  a  harder  and  stronger  metal 
better  suited  than  the  soft  copper  for  the  uses  to  which  these  alloys 
are  applied.  By  the  addition  of  aluminum  or  manganese  in  the 
alloy  the  strong  hard  bronzes  known  as  aluminum  bronze  and 
manganese  bronze  are  produced. 

Iron  and  Steel. — When  iron  ore  is  melted  in  the  furnace  the 
product  obtained,  called  pig  iron,  is  an  alloy  of  iron  with  carbon, 
the  carbon  content  being  about  5  per  cent.  This  alloy  may  be 
readily  fused  and  cast,  and  is  then  called  cast  iron.  By  various 
processes  in  the  furnace  the  amount  of  carbon  in  the  iron  may  be 
reduced.  When  the  quantity  of  contained  carbon  is  between  two 
per  cent  and  two  tenths  of  one  per  cent  the  product  is  steel.  When 
there  is  less  than  two  tenths  of  one  per  cent  of  carbon  we  have 
wrought  iron. 

As  the  amount  of  carbon  is  reduced  the  qualities  of  the  metal 
change  hi  a  marked  degree.  Cast  iron  is  easily  fusible,  is  hard  and 
not  malleable  or  ductile,  cannot  be  welded,  and  has  a  crystalline 
structure.  Wrought  iron,  on  the  other  hand,  is  practically  infusi- 
ble, is  soft,  and  possesses  great  malleability  and  ductility.  It  is 
easily  welded  and  has  a  fibrous  structure. 

The  properties  of  steel  lie  between  those  of  wrought  iron  and 
cast  Iron,  and  the  steel  partakes  of  the  characteristics  of  one  or 
the  other  according  to  the  percentage  of  carbon  contained.  Thus 
low  steel,  that  is,  steel  low  in  carbon,  is  comparatively  soft  and 
may  be  readily  welded  or  drawn  into  wire,  while  high  steels  are 
harder  and  more  brittle  and  weld  with  difficulty. 

CHIEF  CONSTITUENTS. — When  examined  under  the  microscope 
iron  and  steel  are  found  to  be  conglomerate  in  structure,  consisting 


163  ORDNANCE  AND  GUNNERY. 

of  microscopic   particles  chiefly  of  the  following  substances  in 
widely  varying  proportions. 

1.  Pure  or  nearly  pure  metallic  iron,  called  ferrite;  soft,  weak, 
and  very  ductile. 

2.  A  definite  iron  carbide,  Fe3C,  called  cementite,  which  is  ex- 
tremely hard  and  brittle,  but  probably  very  strong  under  a  tensile 
stress. 

The  character  of  the  iron  or  steel  depends  upon  the  proportions 
of  these  two  chief  constituents.  The  steels  which  are  especially 
soft  and  ductile,  as  rivet  and  boiler  plate  steels,  consist  chiefly  of 
the  soft  ductile  ferrite,  the  proportion  of  cementite  in  these  steels 
not  exceeding  perhaps  1  per  cent.  The  harder  steels,  like  rail 
steels,  which  are  called  upon  to  resist  abrasion,  contain  a  much 
larger  percentage  of  cementite,  about  7  per  cent,  and  about  93  per 
cent  of  ferrite.  As  the  proportion  of  cementite  increases  and 
that  of  ferrite  decreases  the  hardness  increases  and  the  ductility 
diminishes.  The  tensile  strength  increases  to  a  maximum  when 
the  cementite  amounts  to  about  15  per  cent  of  the  whole,  and 
then  decreases. 

The  percentage  of  carbon  in  the  metal  is  TV  the  percentage  of 
cementite  the  molecularweightof  Fe3C  being  180,  of  which  12  parts 
are  carbon. 

GRAPHITE.  CAST  IRON. — In  gray  cast  iron  there  is  present,  in 
addition  to  the  ferrite  and  cementite,  a  quantity  of  nearly  pure 
carbon  in  the  form  of  graphite.  The  graphite  is  in  thin  flexible 
sheets  which  form  a  more  or  less  continuous  skeleton  running 
through  the  mass  of  gray  cast  iron.  The  graphite  makes  the  metal 
weak  and  brittle. 

White  cast  iron  contains  but  little  graphite,  but  has  a  much 
higher  percentage  of  cementite  than  either  gray  cast  iron  or  steel. 
The  large  percentage  of  cementite,  over  60  per  cent,  brings  the 
carbon  content  to  about  4£  per  cent,  making  the  iron  extremely 
hard  and  brittle. 

SLAG.  \VROUGHT  IRON. — Wrought  iron  contains,  in  addition  to 
the  matrix  of  ferrite  and  cementite  common  to  all  irons,  a  small 
quantity  of  slag,  a  silicate  of  iron  formed  in  the  process  of  pud- 
dling. The  presence  of  this  slag  forms  the  chief  difference  be- 
tween wrought  iron  and  the  low  carbon  steels. 


METALS   USED  IN  ORDNANCE  CONSTRUCTION.  169 

89.  Hardening  and  Tempering  Steel.— The  distinguishing  char- 
acteristic of  steel  when  compared  with  cast  or  wrought  iron  is  the 
property  it  possesses  of  hardening  when  cooled  quickly  after  being 
heated  to  a  red  heat,  and  of  subsequently  losing  some  of  ite  added 
hardness  when  subjected  to  a  lower  heat. 

There  is  more  or  less  confusion  in  the  use  of  the  terms  applied 
to  the  two  processes.  By  some  the  first  process,  quick  cooling 
from  a  high  heat,  is  called  tempering,  and  the  second  process,  re- 
heating to  a  lower  heat,  is  called  annealing.  By  others  the  first 
process  is  called  hardening  or  quenching,  and  the  second  process, 
which  mitigates  or  lets  down  the  hardness,  is  called  tempering. 
The  more  recent  tendency  is  toward  the  use  of  the  latter 
terms,  and  following  what  is  perhaps  the  better  practice,  we 
will  call  the  first  process  hardening  and  the  second  process 
tempering. 

EFFECT  OF  HEAT. — In  order  to  get  a  comprehensive  idea  of  the 
processes  of  hardening  and  tempering  it  will  be  necessary  to  go 
somewhat  further  into  the  constitution  of  steel  and  to  learn  how 
its  constitution  is  affected  by  heat.  As  before  stated,  the  chief 
constituents  of  steel  are  ferrite  (iron)  and  cementite  (Fe3C). 
These  exist  in  different  proportions,  and  the  behavior  of  the  metal 
under  heat  treatment  is  dependent  to  a  certain  extent  on  the  pro- 
portions of  these  substances.  The  amount  of  carbon  in  the  steel 
depends  on  the  proportion  of  cementite.  The  results  attending 
the  application  of  heat  to  steel  are  chiefly  due  to  the  effect  of  the 
heat  on  the  condition  of  the  carbon. 

Austenite. — When  steel  is  heated  to  a  temperature  of  from  700 
to  1000  degrees  centigrade,  depending  on  the  quantity  of  carbon 
contained,  the  ferrite  and  cementite  of  which  it  is  composed  are 
converted  into  a  substance  called  austenite,  which,  according  to 
Howe,  Professor  of  Metallurgy  in  Columbia  University  and  an 
eminent  writer  on  steel,  is  a  solid  solution  of  carbon  in  iron.  He 
defines  a  solid  solution  as  a  solid  that  bears  the  same  relation  to 
the  definite  solid  chemical  compounds  that  a  liquid  solution,  salt 
water  for  instance,  bears  to  the  definite  liquid  chemical  com- 
pounds, as  water. 

Austenite  is  a  distinct  substance  with  properties  of  its  own. 
When  it  contains  0.75  per  cent  or  more  of  carbon  it  is  extremely 


170  ORDNANCE   AND   GUNNERY. 

hard  and  brittle.  Its  hardness  and  brittleness  are  approximately 
proportional  to  the  percentage  of  carbon  contained. 

The  temperature  at  which  austenite  forms  depends  upon  the 
proportions  of  ferrite  and  cementite  in  the  metal.  When  these 
proportions  are  such  that  there  is  9/10  of  1  per  cent  of  carbon  in  the 
metal,  that  is  when  the  metal  consists  of  0.9x15  =  13.5  per  cent 
of  cementite  and  86.5  per  cent  of  ferrite,  the  transformation  of 
these  constituents  into  austenite  takes  place  at  a  lower  temperature 
than  when  they  are  present  in  any  other  proportions. 

Pearlite.  Eutectoid. — The  mixture  of  ferrite  and  cementite 
containing  0.9  per  cent  of  carbon  is  given  a  specific  name,  pearlite, 
and  is  characterized  as  a  eutectoid,  which  means  a  solid  mixture  in 
the  particular  proportions  that  give  to  the  mixture  the  lowest 
transformation  point  under  the  action  of  heat.  The  corresponding 
term  applied  to  a  liquid  solution  is  eutectic.  Thus  the  eutectic  solu- 
tion of  salt  in  water  contains  23.6  per  cent  of  salt.  When  this 
percentage  of  salt  is  present  the  solution  forms  at  the  lowest  tem- 
perature, and  conversely  the  salt  remains  longest  in  solution  as 
the  temperature  is  lowered. 

Steel  containing  less  than  0.9  of  one  per  cent  of  carbon  is 
considered  to  be  composed  of  pearlite  and  an  excess  of  ferrite, 
while  the  steels  higher  in  carbon  contain  pearlite  and  an  excess  of 
cementite. 

Now  referring  to  Fig.  27  we  will  see  at  what  temperature  the 
various  mixtures  are  transformed  into  austenite.  The  proportions 
of  carbon  and  iron  in  the  metal  are  shown  on  the  horizontal  axis. 
The  curves  are  worded  to  show  the  transformations  that  occur  as 
the  metal  cools  from  the  molten  state. 

When  there  is  0.9  per  cent  of  carbon  in  the  metal  we  have 
pearlite,  which  is  converted  "into  austenite  at  a  temperature  of 
about  680°  C.,  as  shown  in  the  figure  by  the  intersection  of  the  line 
AI  at  the  point  S.  In  the  steels  lower  in  carbon,  which  are  com- 
posed of  pearlite  and  an  excess  of  ferrite,  the  pearlite  is  trans- 
formed at  the  same  temperature  as  before,  but  the  excess  of  ferrite 
requires  a  higher  temperature,  as  shown  by  the  line  SA3,  so  that  the 
transformation  is  not  complete  for  any  particular  composition  until 
that  temperature  is  reached  which  is  indicated  by  the  intersection 
of  the  ordinate  representing  the  composition  with  the  line  SA3. 


METALS   USED  IN  ORDNANCE  CONSTRUCTION. 


171 


1600 

1500- 

1400- 

1300- 

1200- 

1100- 

10002 

A,- 

800° 

700- 

600- 

500- 

400- 

300° 

200- 

100- 
o°c. 


Molten  Cast  Iron 


Anst'enite 


Austenite  and  Graphite  Eutectoid  Forms. 
Austenite  +  Graphite 


Cementite  hegins  to  Form 

Austenite 
4  Cementite 
4  Graphite 


Austsnite  Resolved  into  Ferrite  and  Cementite 


Pearlite 


Ferrite 


Blue 
Oxide 


Straw 
Oxide 


Pearlite 


Cementite 


Pearlite 
4  Cementite 
4  Graphite 


1*5 

I  _< 


! 


I 


I 


Carhon         0.5  1.0  1.5 

Iron  99.0 

Fia.  27. 


2.0  2.5  3.0  3.5  4.0 

98.0  97.0  96.0 

Effect  of  Heat  on  Iron  and  Steel 


-4.5 


5.0 
95.0 


172  ORDNANCE    AND  GUNNERY. 

And  similarly  for  the  higher  carbon  steels  containing  an  excess 
of  cementite;  and  for  the  cast  irons,  which,  containing  more  than 
2  per  cent  of  carbon,  are  composed  of  pearlite,  cementite,  and 
graphite. 

90.  Hardening. — It  will  now  be  easy  to  understand  the  process 
of  hardening  steel  by  means  of  high  heat  followed  by  quick  cooling. 
The  high  heat  causes  the  formation  of  austenite  in  the  metal.  If 
the  metal  is  allowed  to  cool  slowly  the  austenite  is  retransformed 
into  ferrite  and  cementite.  This  transformation  requires  an  ap- 
preciable time,  and  if  the  metal  is  suddenly  cooled  from  its  high 
temperature  the  retransformation  is  prevented,  and  the  hard 
austenite  is  preserved  in  the  cold  metal. 

The  change  in  the  character  of  steel  being  due  principally  to 
the  change  in  the  condition  of  the  carbon  between  its  states  in 
pearlite  and  cementite  and  in  austenite,  the  effect  of  the  heat 
treatment  is  greater  as  the  proportion  of  carbon  in  the  metal  is 
greater.  Thus  the  low-carbon  steels  containing  from  0.06  to  0.10 
per  cent  of  carbon  are  in  general  but  little  affected  by  heat  treat- 
ment and  are  practically  incapable  of  being  hardened,  while  the 
high-carbon  steels  and  some  cast  irons  are  greatly  affected  and  may 
be  given  extreme  hardness. 

The  hardness  and  brittleness  induced  increase  with  the  rapidity 
of  cooling  without  limit,  but  they  are  apparently  nearly  inde- 
pendent of  the  temperature  from  which  the  sudden  cooling  begins, 
provided  that  this  temperature  is  above  the  line  of  complete  trans- 
formation, the  line  A3SE,  Fig.  27.  If  the  metal  is  suddenly  cooled 
from  temperatures  between  the  beginning  and  end  of  the  trans- 
formation, that  is  at  temperatures  between  the  lines  A!  and 
A3SE,  the  hardening  increases  as  the  quenching  temperature  rises. 
The  range  of  temperature  between  the  lines  AI  and  A3SE  is  called 
the  critical  range.  In  this  range  the  hardness  increases  with  the 
quenching  temperature,  but  above  the  critical  range  the  hardness 
is  independent  of  the  temperature. 

The  hardening  of  steel  greatly  increases  its  tensile  strength  and 
elastic  limit,  but  it  makes  the  steel  brittle,  thus  reducing  its  tough- 
ness, as  shown  in  test  pieces  by  reduced  elongation  at  rupture  and 
diminished  contraction  of  area  of  cross  section. 

The  tensile  strength  of  low-carbon  steels  increases  with  the 


METALS   USED  IN  ORDNANCE  CONSTRUCTION. 


173 


rapidity  of  cooling  without  limit.  In  high-carbon  steels  the  ten- 
sile strength  at  first  increases  with  the  rapidity  of  cooling,  but 
reaches  a  maximum  and  then  declines;  that  is,  there  is  a  certain 
rapidity  of  cooling  that  will  give  to  any  one  of  these  steels  its 
maximum  tensile  strength.  This  may  be  due  to  the  fact  that 
rapid  cooling  induces  internal  strains  that  may  become  so  great  as 
to  be  destructive. 

The  following  table,  taken  from  Iron,  Steel,  and  other  Alloys,  by 
Henry  Marion  Howe,  LL.D.,  well  shows  the  effects  of  differences  in 
the  rapidity  of  cooling  of  steel  containing  0.21  per  cent  of  carbon. 


Cooled  in 

Tensile 
Strength. 

Elastic 
Limit. 

Elongation. 

Contraction  of 
Area. 

Iced  brine  

Ibs.  per  sq.  in. 
237,555 

Ibs.  per  sq.  in. 

237,170 

per  cent  in  2  in. 
2   0 

per  cent. 
1   30 

Cold  water  

216,215 

1.5 

1   67 

Oil  

174,180 

2.9 

1  403 

Air  

86,797 

54342 

27  76 

57  829 

In  furnace  

80  103 

44  221 

28  15 

54  749 

91.  Tempering. — Hardened  steel  is  tempered  by  slight  reheat- 
ing, say  to  200°  or  300°  C.  This  process  lessens  the  hardness  and 
brittleness  of  the  steel,  and  thus  increases  its  toughness.  The  aus- 
tenite  of  the  hardened  steel  is  in  a  stable  condition  only  when 
above  the  transformation  temperature.  As  the  temperature  of  the 
steel  diminishes  the  austenite  tends  to  change  into  ferrite  and 
cementite.  In  the  hardening  process  this  tendency  is  resisted  by 
the  frictional  resistance  due  to  the  sudden  cooling,  and  the  aus- 
tenite is  retained  in  an  abnormal  condition  in  the  cold  metal.  The 
reheating  of  the  metal  in  tempering  appears  to  lessen  the  molec- 
ular rigidity  of  the  austenite,  and  to  afford  opportunity  for  part 
of  the  austenite  to  follow  the  course  that  it  would  have  taken  in 
slow  cooling  through  the  transformation  range  and  thus  to  be 
converted  into  pearlite.  The  higher  the  reheating  the  more  does 
the  change  occur. 

The  rate  of  cooling  after  tempering  has  no  effect  on  the  steel, 
since  the  highest  temperature  of  reheating  has  determined  how  far 
the  change  from  austenite  to  pearlite  may  proceed,  and  no  further 
change  can  occur  at  a  lower  temperature.  It  is  therefore  imma- 
terial whether  the  cooling  after  tempering  be  slow  or  rapid. 


174  ORDNANCE  AND  GUNNERY. 

Tempering  has  the  effect  of  reducing  somewhat  the  tensile 
strength  and  elastic  limit  of  hardened  steel,  while  it  increases  its 
toughness,  as  shown  in  test  specimens  by  increased  elongation  at 
rupture  and  increased  contraction  of  area  of  cross-section. 

It  will  be  seen  that  by  proper  regulation  of  the  temperatures  in 
the  processes  of  hardening  and  tempering  an  extensive  control  of 
the  properties  of  the  metal  is  obtained,  permitting  the  production 
of  metal  of  the  quality  best  suited  to  any  particular  purpose. 

The  tempering  temperatures  may  be  judged  within  limits  by 
the  color  given  to  the  steel,  as  it  is  heated,  by  the  various  oxides 
that  form  successively  on  the  surface.  The  following  table  shows 
the  temperatures  at  which  the  colors  appear,  and  the  tempering 
points  for  steels  for  various  purposes. 

220°  C.,  straw;  razors,  surgical  instruments. 

245  yellow;  penknives,  taps,  dies. 

255  brown;  cold  chisels,  hatchets. 

265  brown  with  purple  spots;  axes. 

275  purple;  table  knives,  shears. 

295  violet;  swords,  watch  springs. 

320  blue;  saws. 

525  incipient  red. 

700  dark  red.  . 

950  bright  red. 

1100  luminous  yellow. 

1300  incipient  white. 

1500  white. 

Gun  steel  is  tempered  at  temperatures  between  600°  and  675°  C. 

Annealing. — If  the  steel  after  being  hardened  is  reheated  to  the 
critical  temperature  and  then  cooled  slowly  the  austenite  is  com- 
pletely converted  into  pearlite  and  ferrite  or  cementite,  and  the 
steel  reverts  to  its  original  condition,  losing  all  its  added  hardness 
and  brittleness.  This  process  is  called  annealing. 

92.  Other  Substances. — In  addition  to  the  carbon  in  the  metal, 
there  are  other  substances,  some  of  which  are  always  present  and 
others  that  may  be  added,  that  affect  the  qualities  of  steel. 

Sulphur,  phosphorus,  manganese  and  silicon  are  usually  present 
to  a  greater  or  less  extent  in  all  steels.  If  present  in  too  large  a 


METALS    USED  IN  ORDNANCE  CONSTRUCTION.  175 

percentage  sulphur  produces  what  is  called  hot  shortness  m  the  metal, 
that  is  brittleness  when  hot,  while  phosphorus  makes  the  metal 
cold  short,  or  brittle  when  cold.  Manganese  and  silicon  when 
present  in  proper  percentages  improve  the  qualities  of  the  metal. 

Chromium  and  tungsten  give  hardness  to  the  steel  without 
brittleness. 

Nickel  also  greatly  increases  the  toughness  of  the  steel.  Nickel 
steel  for  guns  contains  about  3|  per  cent  of  nickel. 

Uses. — Cast  iron,  wrought  iron,  cast  steel  and  forged  steel  are 
all  used  in  ordnance  constructions.  Cast  iron  on  account  of  its 
cheapness  and  ease  of  manufacture  in  irregular  shapes  is  used  when 
practicable  wherever  great  strength  is  not  required,  as  in  project- 
iles for  the  smaller  guns  and  in  parts  of  carriages  not  subject  to 
wear  or  to  high  stresses. 

Wrought  iron  is  not  now  extensively  used  in  ordnance  con- 
structions. The  older  seacoast  carriages  were  almost  wholly 
made  of  this  metal. 

Wherever  great  strength  is  required  steel  is  employed.  Cast 
steel  is  used  in  those  parts  that  do  not  require  the  greater  strength 
of  forged  steel,  or  that  on  account  of  their  irregular  shapes  cannot 
be  readily  produced  as  forgings,  such  as  the  chassis  and  top  car- 
riages of  seacoast  gun  carriages.  Cast  steel  has  also  been  used  for 
projectiles  and  for  guns,  but  without  great  success. 

In  structures  or  parts  of  structures  requiring  great  strength,  or 
subject  to  wear,  forged  steel  only  is  used.  Guns  and  armor  and 
armor-piercing  projectiles  are  now  made  of  forged  steel  only,  and 
the  operative  parts  of  gun  carriages  and  of  other  structures  are 
principally  of  this  metal. 

Gun  Steel. — Of  two  steels,  one  high  in  carbon  and  the  other 
low  in  carbon,  the  steel  with  the  higher  percentage  of  carbon  will, 
with  similar  treatment,  have  the  higher  elastic  limit.  Since  the 
elastic  limit  of  the  metal  is  the  limit  of  the  strength  considered  in 
the  construction  of  guns,  it  would  appear  that  the  metal  with  the 
highest  elastic  limit  would  be  the  most  desirable.  But  high  steel 
is  more  difficult  to  manufacture  than  low  steel,  and  in  large  pieces 
there  is  much  greater  liability  to  flaws,  strains,  and  incipient  cracks. 
After  passing  the  elastic  limit  the  hard  steel  has  little  remaining 
strength  and  breaks  without  warning,  wrhile  the  low  steel,  due  to 


176 


ORDNANCE  AND  GUNNERY. 


its  greater  toughness,  yields  considerably  without  fracture.  For 
these  reasons  a  low  steel  containing  about  one  half  of  one  per  cent 
of  carbon  is  used  in  the  manufacture  of  guns. 


MANUFACTURE  OF  STEEL  FORCINGS  FOR  GUNS. 

93.  Open  Hearth  Process.— All  gun  steel  at  the  present  day  is 
made  by  the  open  hearth  process,  which  derives  its  name  from  the 
fact  that  the  receptacle  in  which  the  steel  is  melted  is  open  at 
the  top  and  exposed  to  the  flame  of  the  fuel,  which  plays  over  the 
surface  and  performs  a  principal  part  in  the  formation  of  the  steel. 
The  product  is  called  Siemens  or  Siemens-Martin  steel,  according 
to  the  ingredients  contained. 

The  open  hearth  furnace,  invented  by  Dr.  Siemens,  consists  of 
the  following  essential  parts : 

1.  The  gas  producer; 

2.  The  regenerators; 

3.  The  furnace  proper. 

THE  GAS-PRODUCER. — The  fuel  used  in  the  Siemens  furnace  is 
gaseous,  and  is  obtained  from  ordinary  fuel  by  subjecting  the 

fuel  to  a  preliminary  process 
in  the  gas  producer.  This  ap- 
paratus, Fig.  28,  consists  of 
a  rectangular  chamber  of  fire- 
brick, one  side,  B,  being  inclined 
at  an  angle  of  from  45  to  60  de- 
grees. A  is  the  grate.  The  fuel, 
which  may  be  of  any  kind,  is 
fed  into  the  producer  through 
the  hopper  C.  As  the  fuel  slowly 
burns,  the  COz  rises  through  the 
mass  above  it  and  absorbs  an  additional  portion  of  C,  becoming 
converted  into  2CO.  This  gas  passes  out  of  the  opening  D  into 
a  flue.  In  order  to  cause  it  to  flow  toward  the  furnace  it  is  led 
through  a  long  pipe,  E,  where  it  is  partially  cooled,  and  then  de- 
scends the  pipe  F  leading  to  the  furnace.  The  gas  in  F  being 
cooler  than  that  in  E  and  D,  a  constant  flow  of  gas  from  producer 
to  furnace  is  maintained. 


FIG.  28. 


METALS   USED  IN  ORDNANCE  CONSTRUCTION. 


177 


THE  REGENERATORS. — The  gas  entering  the  furnace  is,  as  has 
been  stated,  CO.  To  burn  it  to  C02,  air  must  be  mixed  with  it. 
This  mixture  is  made  in  the  furnace  proper,  the  CO  and  air  being 
kept  separate  till  they  reach  the  point  where  they  are  to  burn. 
The  CO  is  cooled  to  some  extent,  as  shown,  before  being  admitted 
to  the  furnace. 

To  heat  both  air  and  CO  before  they  are  mixed  and  burned, 
and  to  accomplish  this  economically,  and  raise  the  gases  to  a  high 
temperature,  the  waste  heat  of  the  furnace  is  employed.  The 
heating  of  the  gases  is  accomplished  by  means  of  the  regenerators, 
Fig.  29.  They  consist  of  four  large  chambers,  usually  placed  below 


FIG.  29. 

the  furnace,  filled  with  fire-brick.  The  fire-brick  is  piled  so  that 
there  are  intervals  between  the  bricks  to  allow  the  passage  of  gas 
and  air.  When  the  furnace  is  started,  CO  is  admitted  through  A 
and  air  through  B,  both  A  and  B  being  cold.  The  gases  pass 
between  the  fire-bricks  in  A  and  B  and  through  flues  at  the  top, 
and  flow  into  the  furnace  proper,  where  they  are  lighted.  The 
products  of  combustion  are  caused  to  pass  through  C  and  D, 
which  are  similar  chambers.  In  doing  so  these  products  heat  the 
fire-bricks  in  C  and  D.  After  some  time — about  one  hour  gener- 
ally— by  the  action  of  valves  controlled  by  the  workmen,  the  CO 
and  air  are  caused  to  enter  the  furnace  through  D  and  C  respec- 
tively, and  the  products  of  combustion  to  pass  out  through  A  and 
B.  In  this  case  the  CO  and  air,  entering  the  heated  chambers  D 
and  C,  are  raised  to  a  high  temperature  before  ignition,  and  the 
temperature  of  the  furnace  is  thereby  greatly  increased.  It  is  also 


178 


ORDNANCE  AND  GUNNERY. 


evident  that  A  and  B  will  be  more  highly  heated  than  C  and  D 
were,  and  therefore  when  the  next  change  is  made,  the  gas  and 
air  passing  through  A  and  B  will  be  more  highly  heated  than  when 
they  passed  through  D  and  C,  and  so  on. 

The  action  of  the  furnace  is  therefore  cumulative,  and  ite  only 
limit  in  temperature  is  the  refractoriness  of  the  material.  By 
regulating  the  proportions  of  gas  and  air,  which  is  readily  done, 
the  temperature  may  be  kept  constant. 

94.  THE  FURNACE. — The  furnace  proper,  Fig.  30,  is  a  chamber 
situated  above  the  regenerating  chambers.  The  dish-shaped  cast 


FIG.  30. 

iron  vessel  D,  lined  with  refractory  sand  S,  constitutes  the  hearth 
of  the  furnace.  The  iron  vessel  is  supported  in  such  a  manner 
that  the  air  may  circulate  freely  around  it  and  keep  it  from  melting. 
The  iron  that  is  to  be  converted  into  steel  is  piled  on  the  hearth  of 
the  furnace. 

The  gaseous  fuel  and  air  enter  by  the  flues  F,  and  the  products 
of  combustion  escape  by  the  flues  F',  or  the  reverse,  according  to 
the  position  of  the  regulating  valves.  The  gases  are  ignited  as 
they  enter  the  furnace.  The  sloping  roof  R,  lined  with  fire-brick, 
deflects  the  flames  over  the  metal  on  the  hearth. 

At  opposite  ends  of  the  furnace  are  a  charging  door  for  admis- 
sion of  the  metal,  and  a  tap  hole,  closed  with  a  plug  of  fire-clay, 
for  drawing  off  the  finished  steel. 

OPERATION. — The  process  consists  in  the  decarbonizing  of  cast 
iron  to  the  point  at  which  the  metal  contains  only  that  percentage 
of  carbon  that  is  desired  in  the  steel,  and  in  the  partial  removal 
from  the  iron  of  those  impurities,  such  as  silicon,  manganese,  and 


METALS   USED  IN  ORDNANCE  CONSTRUCTION.  179 

phosphorus,  that  are  injurious  to  the  steel  if  present  in  too  large 
quantities. 

Pig  cast  iron  heated  to  a  red  heat  in  a  separate  furnace  is  piled 
on  the  hearth  of  the  Siemens  furnace,  and  a  quantity  of  steel  or 
wrought  iron  scrap  is  usually  added  to  the  charge  to  reduce  the 
percentage  of  carbon  in  the  mass. 

By  the  action  of  the  furnace  the  charge  is  soon  melted.  Under 
the  influence  of  the  heat  the  carbon  oxidizes  to  carbonic  oxide  gas, 
which  escapes;  the  silicon  oxidizes  to  silica  and  the  manganese  to 
manganous  oxide.  The  silica  and  manganous  oxide  unite  with  the 
slag  which  floats  in  a  thin  layer  on  the  molten  metal. 

The  percentage  of  carbon  in  the  steel  at  any  stage  of  the  proc- 
ess is  determined  by  taking  samples  from  the  metal,  cooling  them, 
and  observing  their  fracture  on  breaking;  and  by  dissolving  por- 
tions of  the  specimens  in  nitric  acid  and  comparing  the  color  with 
the  colors  of  standard  solutions  of  steel  containing  different  per- 
centages of  carbon.  In  this  way  the  composition  of  the  steel  can 
be  exactly  regulated,  for  the  metal  can  be  kept  in  a  melted  state 
without  damage  for  a  considerable  time,  and  the  character  of  the 
flame  can  be  made  oxidizing  or  reducing  at  will,  according  to 
the  relative  amounts  of  air  and  CO  admitted. 

The  decarbonizing  process  is  often  continued  until  the  percent- 
age of  carbon  remaining  in  the  steel  is  less  than  the  percentage 
desired.  The  desired  percentage  is  then  obtained  by  the  addition 
of  pig  iron  containing  a  known  percentage  of  carbon,  such  as 
spiegeleisen  or  ferromanganese,  or  by  the  addition  of  ore. 

The  lining  of  the  hearth,  8  Fig.  30,  is  of  sand  when  the  iron  to 
be  reduced  does  not  contain  a  harmful  percentage  of  phosphorus. 
The  process  is  then  called  the  acid  process,  from  the  silicious  or 
acid  nature  of  the  slag.  When  the  iron  contains  a  larger  percent- 
age of  phosphorus  a  basic  lining,  as  magnesia  or  calcined  dolomite, 
is  required  for  the  removal  of  the  phosphorus.  The  slag  formed  in 
the  basic  process  is  strongly  retentive  of  phosphorus  and  removes 
the  excess  of  this  substance  from  the  metal. 

The  reduction  of  a  charge  of  metal  in  the  Siemens  furnace  or- 
dinarily takes  about  eight  hours. 

When  the  steel  has  attained  its  desired  composition  the  furnace 
is  tapped  and  the  metal  cast  into  ingots. 


180 


ORDNANCE   AND  GUNNERY. 


FIG.  31. 


95-  Other  Processes. — The  crucible  process  is  used  to  some  extent 
by  Krupp  in  the  production  of  gun  steel.  The  ingredients  of  the  steel 
are  melted  together  in  crucibles,  and  the  resulting  steel  is  poured  from 
the  crucibles  into  a  common  reservoir  from  which  the  ingots  are  cast. 
The  Bessemer  Process,  though  important  and  producing  large 
quantities  of  steel,  is  not  used  in  making  gun  steel. 

Casting. — The  molten  metal  is  drawn  into  an  iron  ladle  which 
depends  from  a  crane  in  front  of  the  furnace.  The  ladle,  Fig.  31, 
is  lined  with  refractory  sand.  It  is  provided  with  trunnions,  T', 

so  that  it  may  be  tipped  for  pouring  the 
metal  into  the  mold,  or  it  may  have  a 
tap  hole,  T,  in  the  bottom,  closed  with  a 
plug  of  fire-clay.  The  plug  is  lifted  and 
replaced  by  means  of  a  rod  R  also  encased 
in  refractory  sand.  There  is  an  advan- 
tage in  drawing  the  metal  from  the  bot- 
tom of  the  ladle  in  that  the  scoria  and 
impurities  that  float  on  the  surface  may 
be  kept  out  of  the  mold.  The  metal  if 
very  hot  is  poured  slowly  into  the  mold  in  a  thin  stream,  thus 
allowing  opportunity  for  escape  of 
the  gases  that  it  contains.  If  at 
a  lower  temperature  it  may  be 
poured  more  quickly.  It  is  fre- 
quently allowed  to  cool  to  the 
desired  temperature  in  the  ladle. 

Molds. — In  the  casting  of  ordi- 
nary ingots,  the  iron  or  steel  molds 
into  which  the  metal  is  poured  from 
the  ladle  are  slightly  conical  in 
shape,  Fig.  32,  to  facilitate  their 
removal  from  the  ingot.  They  are 
of  various  cross  sections,  depending 
on  the  shape  of  the  ingot  desired. 
The  interior  surface  is  covered 
with  a  wash  of  clay  or  plumbago. 

Sinking  Head. — In  all  castings,  whether  of  iron,  steel,  or  other 
metal,  an  excess  of  metal,  called  the  sinking  head,  is  left  at  the 


SOLID. 


SPLIT. 


FIG.  32. 


METALS  USED  IN  ORDNANCE  CONSTRUCTION.  181 

top  of  the  mold.  The  pressure  due  to  the  weight  of  this  metal 
gives  greater  density  to  the  casting.  The  sinking  head  also  serves 
to  collect  the  scoria  and  impurities  which  rise  to  the  top,  and 
it  provides  metal  to  fill  any  cracks  or  cavities  that  may  form  in 
the  cooling  of  the  ingot. 

Defects  in  Ingots.  Blow  Holes.— The  gases  in  the  melted 
metal,  unable  to  escape  from  the  mold,  form  holes  in  the  ingot, 
called  blow  holes.  These  cannot  be  detected,  nor  can  they  be  re- 
moved by  forging.  Forging  changes  their  form  only  without  giv- 
ing continuity  to  the  metal.  Blow  holes  are  more  prevalent  in 
Bessemer  than  in  open  hearth  steel  and  are  more  apt  to  occur  at 
low  temperatures  of  casting,  when  the  metal  hardens  before  the 
gas  can  escape. 

Pipes. — The  metal  in  contact  with  the  molds  cools  first  and 
solidifies.  As  the  cooling  and  consequent  contraction  extends 
toward  the  center,  the  liquid  metal  is  drawn  away  from  the  center, 
leaving  cavities  called  pipes  along  the  axis  of  the  ingot.  Pipes 
most  frequently  occur  when  the  metal  is  cast  too  hot.  Thus  on  the 
one  hand  too  low  a  temperature  causes  blow  holes  and  too  high  a 
temperature  pipes. 

Segregation. — As  the  various  constituents  of  the  steel  (iron, 
silicon,  manganese,  etc.)  solidify  at  different  temperatures,  it  fre- 
quently happens  that  the)^  separate  from  each  other  as  the  ingot 
cools,  forming  what  is  called  segregation.  This  gives  a  different 
structure  to  the  metal  and  greatly  weakens  it.  Segregation  is 
more  likely  to  be  found  toward  the  center  of  the  ingot  and  in  the 
upper  portions. 

96.  Whitworth's  Process  of  Fluid  Compression.— The  purpose 
of  this  process,  invented  by  Sir  Joseph  Whitworth  of  England,  is  to 
remove  as  far  as  possible  the  blow  holes,  pipes,  and  other  defects 
from  the  ingot  and  to  give  the  metal  greater  solidity  and  uniformity 
of  structure  than  can  be  obtained  in  the  ordinary  method  of 
casting.  The  object  is  accomplished,  to  a  large  extent,  by  the 
application  of  enormous  pressure  on  the  metal  while  in  the 
fluid  state  in  molds  so  constructed  as  to  allow  free  escape  of 
the  gases. 

The  flask,  /  Fig.  33,  made  of  cast  steel,  is  of  great  strength  to 
withstand  the  great  pressure.  It  is  built  up  of  cylindrical  sections 


182 


ORDNANCE  AND  GUNNERY. 


which  are  bolted  together  to  the  desired  length.  The  interior  of 
the  flask  is  lined  with  vertical  wrought  iron  bars,  6,  whose  long 
edges  are  cut  away  or  beveled  to  form  channels,  a,  by  means  of 
which  the  gas  may  escape:  the  interior  and  exterior  channels 

thus  formed  being  connected  by 
grooves,  c,  cut  in  the  sides  of  the 
bars  at  short  intervals.  The  cylin- 
der formed  by  the  interior  surfaces 
of  the  bars  is  lined  with  refractory 
sand.  A  cast  iron  plate,  d,  through 
which  are  continued  the  longitudi- 
nal gas  channels  closes  the  mold  at 
the  bottom.  The  mold  rests  on  a 
car  in  the  bottom  of  a  pit. 

When  the  mold  is  rilled  with 
metal  the  car  is  run  into  a  hydraulic 
press  with  an  adjustable  head.  The 
head,  p,  of  the  press,  of  diameter 
only  slightly  less  than  the  interior 
of  the  mold,  is  brought  down 
against  the  molten  metal  and 
locked  in  that  position.  The  metal 
wells  up  around  the  head  of  the 
press  and,  quickly  cooling,  forms 
a  solid  mass  which  with  the  head 
completely  closes  the  top  of  the 
mold. 

The  press  is  constructed  with  its 
piston  at  the  bottom  so  that  the 
pressure  may  be  applied  on  the 
bottom  of  the  car  that  carries  the 
mold. 

By  the  pressure  on  the  bottom 
of  the  car,  gradually  applied  until 
a  pressure  of  six  tons  to  the  square 
inch  is  reached,  the  car  and  mold  are  slowly  forced  upward. 
The  molten  metal  is  compressed  by  the  applied  pressure,  and  the 
gas,  forced  through  the  sand  lining  and  the  channels  between 


B 

J 

-r  —  - 

JL 

1 
' 

a 
a 

-b 

JJ 

a 

- 

a 

'_ 

a 

f 

| 

a 

~ 

a- 

a 

-a 

^ 

a 

I 

E 

3 

c 

IP 

K\ 

ID 

C 

a 

.b 

e 

- 

D 

C 

a 

a 

C 

a 

[ 

a 

r 

[ 

n 

D  r 

a 

D 

0^ 

1 

tl 

4 

FIG.  33. 


METALS  USED  IN  ORDNANCE  CONSTRUCTION.  183 

the  lining  bars,  issues  from  the  top  and  bottom  of  the  mold 
in  a  violent  flow  of  flame.  The  pressure  is  continued  until 
the  column  of  metal  has  shortened  one  eighth  of  its  length. 
A  uniform  pressure  of  about  1500  pounds  to  the  square  inch  is 
then  left  on  the  ingot  while  it  cools,  to  follow  up  the  metal  as 
it  contracts  and  prevent  the  formation  of  cracks. 

97.  Processes  After  Casting. — The  specifications  for  gun  forg- 
ings  require  that  the  forgings  be  made  from  that  part  of  the  ingot 
that  remains  after  30  per  cent  by  weight  has  been  cut  from  the 
top  of  the  ingot  and  6  per  cent  from  the  bottom.  These  parts 
are  cut  off,  as  they  are  likely  to  contain  most  of  the  defects  in 
the  ingot. 

For  hollow  forgings  the  center  of  the  part  selected  is  then  bored 
out  in  a  heavy  lathe,  or  punched  out  if  the  ingot  is  short. 

Heating. — The  ingot  is  then  heated  preparatory  to  forging. 
The  heating  is  accomplished  in  a  furnace  erected  near  the  forging 
hammer  or  press,  and  is  conducted  with  great  care.  The  cooling 
of  the  ingot  in  the  mold  has  left  in  the  metal  strains  due  to  the 
successive  contraction  of  the  interior  layers.  Assisted  by  unequal 
expansion  in  heating  the  strains  may  cause' cracks  to  develop  in  the 
ingot.  Great  care  is  therefore  exercised  that  the  heating  shall  pro- 
ceed slowly  and  uniformly,  thus  avoiding  the  overheating  of  the 
exterior  layers  of  metal  before  the  heat  has  thoroughly  penetrated 
to  the  interior. 

Forging. — The  heated  ingot  is  forged  either  by  blows  delivered 
by  a  steam  hammer  or  by  pressure  delivered  by  a  hydraulic  forg- 
ing press.  Under  the  slow  pressure  of  the  forging  press  the  metal 
of  the  forging  has  more  time  to  flow,  the  effect  of  the  treatment  is 
more  evenly  distribnted,  and  the  metal  is  more  uniformly  strained. 
This  process  is  therefore  preferred  in  the  manufacture  of  gun 
forgings. 

Fig.  34  is  a  reproduction  from  a  photograph  of  a  5000-ton 
hydraulic  forging  press  at  the  works  of  the  Bethlehem  Steel  Co. 
The  print  shows  a  bored  ingot  for  the  tube  of  a  12-inch  gun  being 
forged  on  a  mandrel.  The  outer  diameter  of  the  ingot  is  reduced 
by  the  forging  and  the  length  of  the  ingot  increased.  The  diameter 
of  the  bore  remains  practically  unchanged.  The  outer  end  of  the 
ingot  is  supported  from  an  overhead  crane. 


184  ORDNANCE  AND  GUNNERY. 

The  ingot  is  turned  on  the  anvil  of  the  press,  and  advanced  when 
desired,  by  means  of  the  chain  seen  through  the  press.  The  method 
of  turning  is  better  shown  in  the  plate  following. 

The  movements  of  the  head  of  the  press  are  controlled  by  means 
of  levers  situated  at  a  short  distance  to  the  right  of  the  press.  The 
operator  at  the  lever  sees  recorded  on  the  dial  the  pressure  exerted 
at  any  instant. 

Fig.  35  shows  a  10-ton  steam  hammer  forging  a  solid  ingot  for 
a  3-inch  gun.  The  ingot  is  supported  from  an  overhead  crane  and 
is  nearly  balanced  in  the  sling  chain  by  the  bar  of  iron,  called  a 
porter  bar,  clamped  to  the  ingot  and  extending  to  the  rear.  By 
bearing  down  on  the  porter  bar  the  ingot  is  lifted  off  the  anvil  and 
may  then  be  moved  by  the  crane  back  and  forth  under  the  ham- 
mer. The  ingot  is  turned  under  the  hammer  from  the  crane  by 
means  of  the  gearing  shown  in  the  upper  part  of  the  picture. 

The  movements  of  the  hammer  are  controlled  by  the  man  at  the 
left  through  the  levers  shown  at  his  hand. 

98.  Hollow  Forgings. — In  forging  bored  ingots  a  solid  steel 
shaft  called  a  mandrel  is  passed  through  the  bore  of  the  heated 
ingot,  and  the  method  pursued  in  forging  depends  upon  whether 
the  length  of  the  ingot  is  to  be  increased  without  change  of  interior 
diameter,  as  in  forging  a  gun  tube,  or  whether  the  diameters  of  the 
ingot  are  to  be  enlarged,  as  in  forging  hoops.  In  the  first  case  the 
ingot,  on  a  mandrel  of  proper  diameter,  is  placed  directly  on  the 
anvil  of  the  press,  as  shown  in  Fig.  34.  The  effect  of  forging  is 
then  to  increase  the  length  of  the  ingot  and  decrease  the  outer 
diameter  while  maintaining  the  interior  diameter  unchanged. 
The  mandrel  is  withdrawn  from  the  forging  by  means  of  a 
hydraulic  press. 

In  forging  hoops,  the  mandrel  rests  on  two  supports  on  either 
side  of  the  head  of  the  press,  Fig.  36,  and  is  itself  the  anvil  on 
which  the  forging  is  done.  By  turning  the  mandrel  new  surfaces 
of  the  hoop  are  presented  to  the  press.  The  walls  of  the  hoop  are 
reduced  in  thickness  by  the  forging,  the  diameters  of  the  hoop 
being  increased,  while  the  length  is  not  materially  changed. 

The  specifications  for  gun  forgings  require  that  the  part  of  a 
solid  ingot  used  for  a  tube  forging  shall  have  before  forging  an 
area  of  cross  section  at  least  four  times  as  great  as  the  maximum 


FIG.  34. — 5,000-ton  Hydraulic  Forging  Press. 


METALS  USED   IN  ORDNANCE  CONSTRUCTION. 


185 


area  of  cross  section  of  the  rough  forging  when  finished,  and  for  a 
jacket  forging  3|  times  as  great.  For  forgings  for  guns  12  inches 
or  more  in  caliber  these  figures  are  reduced  to  3£  and  3  respectively. 
Forgings  for  lining  tubes  must  be  reduced  6  times  in  area. 

If  bored  ingots  are  used  the  wall  of  the  ingot  must  be  reduced 
at  least  one  half  in  thickness. 

Annealing. — The  working  of  the  ingot  in  forging  and  the  irreg- 
ular cooling  leaves  the  metal  in  a  state  of  strain.  The  strains 
are  removed  by  the  process  of  annealing.  For  this  purpose  the 


if 


1 

f 

\v~_-'y 

FRONT    ELEVATION. 


SIDE  ELEVATION. 


FIG.  3fi. 


forging  is  usually  laid  in  a  brick-walled  pit  or  furnace,  and  slowly 
and  uniformly  heated  by  wood  fires,  the  burning  logs  being  dis- 
tributed along  the  pit  as  required  to  heat  the  forging  uniformly. 
When  the  proper  heat,  usually  a  bright  red,  has  been  attained,  the 
fires  are  allowed  to  die  out,  or  are  drawn,  and  the  ingot  remains 
in  the  furnace  until  both  are  cold.  Three  or  four  days  may  be 
required  for  the  slow  cooling  of  a  large  forging. 

99.  Hardening  in  Oil  or  Water. — Annealing  removes  the  in- 
ternal strains  that  exist  in  the  forging,  but,  as  before  explained,  it 
greatly  reduces  the  tensile  strength  and  elastic  limit  of  the  metal. 
To  restore  the  strength  to  the  metal  and  to  produce  in  it  the  quali- 
ties required  in  gun  forgings,  the  forging  is  next  subjected  to  the 
process  of  hardening.  Before  hardening  it  is  machined  in  a  lathe 
nearly  to  finished  dimensions.  Specimens  for  tests  are  cut  from 
the  ends,  and  from  their  behavior  in  the  testing  machine  the  re- 
quirements of  the  subsequent  treatment  are  determined. 


186  ORDNANCE  AND  GUNNERY. 

The  forging  is  then  slowly  and  uniformly  heated  throughout. 
Large  forgings,  such  as  tubes  and  jackets,  are  heated  in  vertical 
furnaces,  great  care  being  exercised  that  the  heating  shall  be  uni- 
form throughout  the  length  of  the  piece  in  order  that  undue  warp- 
ing may  not  occur  in  the  subsequent  cooling.  When  the  forging 
is  at  a  uniform  red  heat  the  side  of  the  furnace  is  opened  and  the 
forging  is  lifted  out  by  a  crane  and  immersed  in  a  deep  tank  of  oil 
or  of  water  alongside  the  furnace.  The  oil  tank  is  surrounded  by 
another  tank  through  which  cold  water  is  constantly  running. 
The  heat  of  the  forging  passes  to  the  oil  and  thence  to  the  water, 
and  is  thus  gradually  conducted  away. 

The  Bethlehem  Steel  Co.  of  Bethlehem,  Penn.,  and  the  Midvale 
Steel  Co.  of  Philadelphia,  the  two  principal  manufacturers  of  gun 
forgings  in  this  country,  use  different  oils  for  oil  tempering.  The 
Bethlehem  Co.  uses  petroleum  oil  once  refined.  The  Midvale  Co. 
uses  cottonseed  oil  with  flashing  point  not  less  than  360  degrees 
centigrade. 

The  temperature  of  the  forging  when  immersed  is  very  high 
compared  with  that  of  the  oil.  The  cooling  is  therefore  sudden  at 
first,  but  as  oil  is  a  poor  conductor  of  heat  the  heat  of  the  forging 
is  carried  away  slowly,  leaving  the  metal  with  greater  toughness 
than  it  would  have  if  hardened  in  water  and  cooled  more  quickly. 

Oil  is  customarily  used  in  the  hardening  of  gun  forgings.  Occa- 
sionally the  qualities  of  the  metal  are  such  that  better  results  are 
obtained  by  the  quicker  cooling  in  water. 

Tempering. — The  process  of  hardening  greatly  increases  the 
elastic  strength  of  the  metal  but  reduces  its  toughness.  At  the 
same  time  it  produces  internal  strains  due  to  contraction  in  cool- 
ing. The  strains  are  removed,  the  hardness  reduced,  and  the 
toughness  restored  by  the  process  of  tempering,  conducted  in  the 
same  manner  as  the  previous  annealing,  but  at  a  lower  heat,  so 
that  the  gain  in  elastic  strength  is  reduced  but  slightly  and  not 
entirely  lost.  The  tempering  temperature  for  gun  forgings  lies 
between  600  and  675  degrees  centigrade,  1100  to  1250  degrees 
Fahrenheit. 

Specimens  are  again  taken  from  the  ends  of  the  forging  and 
broken  in  the  testing  machine.  If  the  specimens  do  not  fulfil  the 
requirements  of  the  specifications  the  forging  is  again  hardened 


METALS   USED  IN  ORDNANCE  CONSTRUCTION.  187 

and  tempered,  the  temperature  and  conduct  of  the  processes  being 
so  regulated  as  to  improve  those  qualities  in  which  the  metal  has 
proved  defective  in  the  tests. 

Strength  of  Parts  of  the  Gun. — The  requirements  in  steel  forg- 
ings  for  guns  over  8  inches  in  caliber  are  shown  in  the  table  on 
page  165.  It  will  be  observed  that  the  strength  of  the  metal  in- 
creases as  we  proceed  outward  from  the  center  of  the  gun.  Thus 
the  elastic  limit  of  the  tube  is  46,000  Ibs.,  of  the  jacket  48,000,  and 
of  the  hoops  53,000.  It  would  be  better  if  the  strongest  metal 
were  in  the  tube,  which  has  to  endure  the  greatest  strain.  But  the 
production  of  the  high  qualities  required  is  much  more  difficult  in 
large  forgings  than  in  smaller  ones,  and  for  this  reason  the  require- 
ments for  the  tubes  and  jackets  must  be  lower  than  for  the  hoops. 
An  additional  reason  for  the  difference  in  requirements  is  found  in 
the  fact  that  the  metal  of  the  tube  has  the  advantage  of  greater 
elongation  before  rupture,  as  may  be  seen  in  the  table  on  page 
165.  The  greater  elongation  is  difficult  to  produce  with  the  higher 
elastic  limit. 

The  tubes  and  jackets  of  guns  under  8  inches  in  caliber  have 
an  elastic  limit  of  50,000  Ibs. 

Forged  steel  that  has  an  elastic  limit  of  over  110,000  Ibs.  is  now 
produced. 


CHAPTER  VI. 
GUNS. 

ELASTIC  STRENGTH  OF  GUNS. 

100.  The  Elasticity  of  Metals. — In  the  chapter  on  metals  the 
elastic  limit  of  a  metal  has  been  defined  as  the  minimum  stress  per 
unit  of  area  of  cross  section  that  will  produce  in  the  metal  a  per- 
manent set.  For  each  kind  of  stress,  whether  of  extension  or  com- 
pression, the  metal  has  a  distinct  elastic  limit.  The  elastic  limit  of 
extension,  or  the  tensile  elastic  limit,  is  usually  less  than  the  elastic 
limit  of  compression.  In  gun  steels  the  difference  is  not  great  and 
the  two  are  considered  equal.  The  tensile  elastic  limit  is  ordi- 
narily used,  as  it  is  the  limit  usually  measured. 

Hooke's  Law. — A  tensile  stress  applied  to  a  bar  of  metal  causes 
elongation  of  the  bar,  and  it  is  found  by  experiment  that  under 
stresses  less  than  the  elastic  limit  of  the  metal  the  elongation  is 
proportional  to  the  stress.  In  other  words,  within  the  elastic  limit 
of  the  metal  the  ratio  of  the  stress  to  the  strain  is  constant.  This 
law  is  known  as  Hooke's  law,  and  is  often  expressed  ui  tensio  sic 
vis. 

Modulus  of  Elasticity. — If  we  measure  the  elongation  of  a  bar 
caused  by  a  tensile  stress,  and  divide  the  measured  elongation  by 
the  original  length  of  the  bar,  we  will  obtain  the  elongation  per 
unit  of  length,  expressed  as  a  numerical  fraction. 

Now  if  we  divide  any  stress  per  unit  of  area  within  the  elastic 
limit  of  the  metal  by  the  elongation  per  unit  of  length  the  result 
will  be  the  constant  ratio  of  stress  to  strain  within  the  elastic  limit. 
This  ratio  is  called  the  modulus  of  elasticity. 

Let  E  be  the  modulus  of  elasticity  of  the  metal, 
0  the  elastic  limit  of  the  metal, 
f  the  elongation  per  unit  of  length  at  the  elastic  limit. 

188 


GUNS.  189 

By  definition  we  have 


If  we  assume  that  the  elasticity  of  the  metal  continues  in- 
definitely we  see,  by  making  7-  equal  to  unity  in  the  above  equa- 
tion, that  the  modulus  of  elasticity  is  the  stress  per  unit  of  area 
that  would  extend  a  bar  to  twice  its  length. 

When  the  elastic  limit  is  expressed  in  pounds  per  square  inch 
the  modulus  of  elasticity  of  steel  may,  without  sensible  error,  be 
taken  as  30,000,000. 

The  modulus  of  elasticity  is  really  a  stress  per  unit  of  area,  but 
it  had  best  be  considered  as  the  abstract  ratio  between  stress  and 
strain. 

Since  by  Hooke's  law  the  ratio  of  the  stress  to  the  strain  is  con- 
stant within  the  elastic  limit,  we  may  write  for  6  and  f  in  equa- 
tion (1)  any  other  stress  within  the  elastic  limit  and  its  correspond- 
ing strain. 

Let  S  be  a  stress  per  unit  of  area  within  the  elastic  limit, 
I  the  strain  per  unit  of  length  due  to  the  stress. 

Then  E  =  S/l    and    l  =  S/E  (2) 

That  is,  the  strain  per  unit  of  length  due  to  any  stress  per  unit 
of  area  within  the  elastic  limit  is  equal  to  the  stress  divided  by  the 
modulus  of  elasticity. 

101.  Strains  Perpendicular  to  the  Direction  of  the  Stress.  — 
In  the  previous  paragraphs  we  have  considered  only  the  strain 
produced  in  the  direction  of  the  stress.  But  we  have  seen  in  the 
chapter  on  metals  that  a  tensile  stress  produces  a  reduction  in  area 
of  cross  section,  and  it  is  found  by  experiment  that,  for  steel,  the 
strain  at  right  angles  to  the  direction  of  a  stress  within  the  elastic 
limit  of  the  metal  is  equal  to  one  ^  ^ 

third  of  the  strain  in  the  direction  of  a          t 

the  stress.  If  the  cube  in  Fig.  37  is 
subjected  to  the  tensile  stress  repre- 
sented by  p,  the  edges,  aa,  bb,  etc., 


dL 


parallel  to  the  direction  of  the  stress  FlG  37> 

will  be  elongated,  and  the  edges,  ab, 

ac,  etc.,  perpendicular  to  this  direction  will  be  shortened  by  an 

amount  equal  to  one  third  the  elongation  of  the  parallel  edges. 


- 
E\        3      3 


190  ORDNANCE  AND  GUNNERY. 

Equations  of  Relation  between  Stress  and  Strain. — If  we  con- 
sider that  the  cube  is  subjected  at  once  to  tensile  stresses  applied 
in  the  three  directions  perpendicular  to  its  faces,  the  strain  in  each 
direction  due  to  the  stress  in  that  direction  will  be  diminished  by 
the  contrary  strains  due  to  the  perpendicular  stresses. 

Let  X,  Y,  and   Z  be  three   independent  extraneous  tensile 
forces  perpendicular  to  the  faces  of  the  cube; 
lx,  ly,  and  lz  the  strains  in  the  directions  of  X,  Y,  and  Z  re- 
spectively. 
The  strain  in  the  direction  X  due  to  the  force  X  is  from  equa- 

1  Y  1  Z 

tion  (2)  X/E.    It  is  diminished  by  ^-^  and  by  ^  -^.    Therefore, 

for  the  total  strains  in  the  three  directions,  we  have 


(3) 


Problems.  1.  A  steel  test  specimen  has  an  elastic  limit  of 
59,000  Ibs.  What  will  be  its  elongation  per  unit  of  length  at  the 
elastic  limit?  0.00197 

2.  The  original  diameter  of  the  specimen  being  0.505  inches, 
what  is  its  diameter  when  the  piece  is  stretched  to  its  elastic  limit? 

0.5047  inches. 

3.  A  vertical  steel  rod  20  feet  long  and  J  inch  square  sustains 
at  its  lower  end  a  load  of  6000  Ibs.    The  elastic  limit  of  the  steel  is 
72,000  Ibs.     What  will  be  the  elongation  caused  by  the  load? 

0.192  inches. 

4.  Taking  the  modulus  of  elasticity  of  copper  as  16,000,000, 
what  will  be  the  elongation  of  a  copper  bar  1  inch  square  and  10 
feet  long  supporting  a  load  of  5000  Ibs.?  0.0375  inches. 

102.  Principal  Stresses  and  Strains. — Since  every  stress  applied 
to  a  solid  produces  stresses  in  directions  perpendicular  to  the  direc- 
tion of  the  applied  stress,  at  any  point  in  a  solid  under  stress  there 
are  always  three  planes  at  right  angles  to  each  other  upon  each  of 


GUNS.  191 

which  the  stress  is  normal.  Thus  in  the  cube  we  have  just  con- 
sidered, the  stresses  at  any  point  in  the  cube  are  normal  to  three 
planes  parallel  to  the  faces  of  the  cube.  The  normal  stresses  are 
called  the  principal  stresses  at  the  point;  and  it  may  be  shown  by 
the  ellipsoid  of  stress  that  one  of  the  principal  stresses  is  the  great- 
est stress  at  the  point.  The  corresponding  strains  are  called  the 
principal  strains. 

Stresses  and  Strains  in  a  Closed  Cylinder. — The  following  dis- 
cussion of  the  elastic  strength  of  cylinders  is  based  on  the  theory 
of  Clavarino,  published  in  1879,  and  modified  through  the  results 
of  experiments  by  Major  Rogers  Birnie,  Ordnance  Department, 
U.  S.  Army. 

Consider  a  hollow  metal  cylinder,  closed  at  both  ends,  to  be 
subjected  to  the  uniform  pressure  of  a  gas  confined  in  the  cylinder. 
The  pressure  acting  perpendicularly  to  the  cylindrical  walls  will 
tend  to  compress  the  walls  radially.  If  we  consider  a  longitudinal 
section  of  the  cylinder  by  any  plane  through  the  axis,  the  pressure 
acting  in  both  directions  perpendicular  to  this  plane  will  tend  to 
disrupt  or  pull  apart  the  cylinder  at  the  section,  and  will  therefore 
produce  a  tensile  stress  in  a  tangential  direction  on  the  metal 
throughout  the  section.  The  pressure  acting  against  the  ends  of 
the  cylinder  will  tend  to  pull  it  apart  longitudinally. 

The  metal  of  any  elementary  cube  in  the  cylinder  is  therefore 
subjected  to  three  principal  stresses :  a  radial  stress  of  compression, 
a  tangential  stress  of  extension,  and  a  longitudinal  stress  of  ex- 
tension. 

If  the  cylinder  be  subjected  to  a  uniform  exterior  pressure 
stresses  will  be  similarly  developed  in  the  three  directions. 

In  the  following  discussion  we  will  always  understand  by  the 
term  stress,  the  stress  per  unit  of  area,  and  b)'  the  term  strain,  the 
strain  per  unit  of  length,  unless  these  terms  are  qualified  by  the 
word  total  or  other  qualifying  word. 

Assume  a  closed  cylinder  affected  by  uniform  interior  and  ex- 
terior pressures.  At  any  point  of  the  cylinder 

Let  i  be  the  tangential  stress, 
p  the  radial  stress, 
q  the  longitudinal  stress. 

Substituting  these  letters  in  equations  (3)  for  X,  Y,  and  Z, 


192  ORDNANCE  AND  GUNNERY. 

respectively,  and  changing  the  sign  of  Y,  since  the  interior  and 
exterior  pressures  act  toward  each  other  radially,  so  that  the 
stress,  p,  acts  in  a  direction  opposite  to  that  assumed  for  Y  in 
deducing  equations  (3),  we  obtain  the  following  equations. 


_          1/M.P  t\ 

t~     E\t+3      3/ 


which  express  the  values  of  the  strains  in  the  directions  of  the 
three  stresses.  These  values  may  be  positive  or  negative,  depend- 
ing upon  the  resultant  of  the  stresses.  A  positive  value  of  a  strain 
represents  elongation  and  a  negative  value  contraction,  as  a  posi- 
tive value  of  a  stress  represents  a  tensile  stress  and  a  negative 
value  a  compressive  stress. 

103.  Relations  between  the  Stresses  t,  p,  and  q.  Lamp's 
Laws.  —  The  stresses  and  strains  in  equations  (4)  form  six  unknown 
quantities  which  cannot  be  determined  from  the  three  equations. 

Lame,  a  distinguished  investigator  in  the  subject  of  elasticity 
of  solid  bodies,  has  established  relations  between  the  stresses,  by 
means  of  which  the  equations  may  be  solved  and  the  values  of  the 
stresses  and  strains  determined.  He  assumes  that  the  longitudinal 
stress  q  and  the  longitudinal  strain  lq  are  constant  throughout  the 
cross  section.  The  last  of  equations  (4)  may  then  be  written 

t—  p  =  3(q—  lqE)  =  constant  (5) 

which  equation  is  true  whether  q  has  a  value  or  is  zero.  As  t  and 
p  apply  to  any  point  in  the  walls  of  the  cylinder,  we  have  Lame's 
first  law. 

In  a  cylinder  under  uniform  pressure  the  difference  between  the 
tangential  tension  and  the  radial  pressure  is  the  same  at  all  points 
in  the  section  of  the  cylinder. 


GUNS. 


193 


Now  let  us  consider  a  right  section  of  the  cylinder,  of  unit 
length,  Fig.  38. 

Let  P0  be  the  pressure  per  unit  of 
area  acting  on  the  in- 
terior of  the  cylinder, 
PI  the  pressure  per  unit  of 

area  on  the  exterior, 
Ro  the  interior  radius  of  the 

cylinder, 

#1  the  exterior  radius, 
r  the  radius  of  any  point  hi 

the  cylinder. 

The  total  interior  pressure  acting 
normally  on  either  side  of  the  diametral  plane  be  is  2P0Ro.  The 
total  pressure  acting  on  the  outer  circumference  on  either  side  of 
the  plane  and  normal  to  it  is  2P\R\.  The  difference  of  these  pres- 
sures is  the  resultant  pressure  acting  on  the  metal  in  the  sectional 
plane  be.  The  total  tangential  stress  on  the  metal  at  the  section 
will  therefore  be 


FIG.  38. 


But  since  t  represents  this  stress  per  unit  of  area,  the  total 

fRi 

stress  is  equal  to  2  /     t  dr.    Therefore 
JRO 

J  Ro 


R0 

Assuming  that  t  is  a  function  of  r,  it  must  be  such  a  function 
that  t  dr  when  integrated  between  the  limits  R\  and  R0  will  be 
equal  to  P0R0—PiRi.  t  dr  must  then  be  equal  to  —d(pr)  because 
the  integral  of  this  expression  taken  between  the  given  limits  is 
P0R0—PiRi.  The  substitution  of  the  pressures  P0  and  PI  for  the 
radial  stress  p,  in  integrating  the  expression  —d(pr),  may  be  made 
because,  as  will  be  found  later,  p  varies  proportionately  with  P0 
and  PL 

We  therefore  have 


tdr  =  d(pr)  =  —  p  dr—dpr, 


194  ORDNANCE  AND  GUNNERY. 

From  which  by  combination  with  equation  (5)  and  integration, 
see  foot  note,  we  obtain 

t+p  =  C/r>  (6) 

in  which  C  is  a  constant. 

Equation  (6)  expresses  Lame's  second  law: 

In  a  cylinder  under  uniform  pressure  the  sum  of  the  tangential 
tension  and  the  radial  pressure  varies  inversely  as  the  square  of  the. 
radius. 

Both  laws  are  based  on  the  assumption  that  the  longitudinal 
stress  is  constant  or  zero. 

104.  Stresses  in  the  Cylinder.  —  By  means  of  Lame's  laws  we 
may  now  determine  the  values  for  the  stresses  at  all  points  in  the 
cylinder.  We  may  write  for  t,  p,  and  r  in  equations  (5)  and  (6) 
the  coordinate  values  referring  to  any  point  in  the  cylinder  and 
thus  form  the  equations 


Eliminating  TO  and  TI  from  these  equations  we  may  obtain 


P0R02-P1R12        flo  _ 

Ri2-R02  Ri2-R02         2 


r  /?,2_/?_2  /?,2_   ft  -2  r2 

il/1         .tt/0  "1         «0  ' 

t  dr—  —pdr  —  rdp 
—  (t+p)dr=rdp 
From  equation  (5)  t+p=2p+k 

Therefore  = — ^-T 

r       '2p+k 

Integrating 

loge  -=  jloge  (2p+fc)  +  loge  A 
Replacing  2p+  k  by  its  value  t  +  p  we  obtain 


or  «+p=l/AVJ 


GUNS.  195 

From  these  equations  we  may  obtain  the  values  of  the  tangen- 
tial and  radial  stresses  at  any  point  in  the  section  of  the  cylinder 
by  substituting  for  r  its  value  for  the  point. 

Longitudinal  Stress.  —  The  longitudinal  stress  has  been  as- 
sumed as  constant  over  the  cross  section  of  the  cylinder.  Under 
this  assumption  when  applied  to  a  gun  the  total  longitudinal 
stress  due  to  the  pressure  on  the  face  of  the  breech  block  is  dis- 
tributed uniformly  over  the  cross  section  of  the  gun,  producing  a 
stress  per  unit  of  area  that  is  small  compared  with  the  tangential 
and  radial  stresses.  In  the  present  discussion  of  the  stresses  act- 
ing on  the  cylinder  the  longitudinal  stress  will  therefore  be  neg- 
lected, and  q  in  equations  (4)  will  be  considered  as  zero.  Later 
the  value  of  the  longitudinal  stress  will  be  deduced. 

105.  Resultant  Stresses  in  the  Cylinder.  —  Making  g  =  0  ir± 
equations  (4)  and  substituting  for  i  and  p  their  values  from  (7)  and 
(8)  we  obtain 

±Ro2Ri2(Po-Pi)I 


*-Jit 

Elp 

Wl 

"3       RS-Ro2 
„      2P0R02-P1Rl2 

3       Ri2-R02       r2 

v.»; 
(10) 
rm 

"p    3      Ri2-R02 

3      ^i2  —  Ro2        r2 

In  the  above  equations  the  first  members  are  the  respective 
strains  multiplied  by  the  modulus  of  elasticity.  Referring  to 
equation  (2)  we  see  that  each  product  is  equal  to  the  stress  which 
acting  alone  would  produce  the  strain.  The  equations  then  give 
the  values  of  the  simple  stresses  that  would  produce  the  same 
strains  as  are  caused  by  the  stresses  p  and  t  acting  together.  Their 
values  at  any  point  in  the  cylinder  are  obtained  from  the  above 
equations  by  giving  to  r  the  value  for  the  point. 

Basic  Principle  of  Gun  Construction.  —  The  following  principle 
is  the  foundation  of  the  modern  theory  of  gun  construction. 

No  fiber  of  any  cylinder  in  the  gUn  must  be  strained  beyond  the 
elastic  limit  of  the  metal  of  the  cylinder. 

This  principle  is  strictly  adhered  to  in  the  construction  of  guns 
built  up  wholly  of  steel  forgings.  In  the  construction  of  wire- 


196  ORDNANCE  AND  GUNNERY. 

wound  guns  the  tube  is,  in  some  constructions,  purposely  com- 
pressed beyond  its  elastic  limit  by  the  pressure  exerted  upon  it  by 
the  wire. 

The  principle  fixes  a  limit  to  the  stresses  to  which  any  cylinder 
that  forms  part  of  a  gun  may  be  subjected.  If  we  represent  by 

6  the  tensile  elastic  limit  of  the  metal, 

p  the  compressive  elastic  limit  of  the  metal, 

the  stresses  represented  by  the  first  members  of  equations  (9)  to 
(11)  may  never  exceed  either  6  or  p,  depending  on  whether  the 
stress  is  one  of  extension  or  of  compression;  and  the  interior  and 
exterior  pressures,  represented  by  P0  and  PI  in  those  equations, 
must  never  have  such  values  as  to  cause  the  stresses  to  exceed  these 
limits. 

1 06.  Simplification  of  the  Formulas  of  Gun  Construction. — 
The  formulas  of  gun  construction  are  deduced  from  equations  (9), 
(10),  and  (11).  Heretofore,  in  the  deduction,  these  equations  have 
been  used  in  the  form  in  which  they  appear  above,  and  the  for- 
mulas resulting  from  them  have  been  similarly  extended  and 
equally  formidable  in  appearance,  and  much  labor  has  been  ex- 
pended in  writing  them  out. 

We  will  introduce  here,  for  the  first  time  in  any  text,  a  sim- 
plification of  equations  (9),  (10),  and  (11),  which  will  result  in  a 
marked  simplification  of  all  the  formulas  of  gun  construction, 
making  the  formulas  easier  to  handle,  and  greatly  reducing  the 
labor  required  in  their  use. 

We  will  express  in  equations  (9),  (10),  and  (11)  R\2  in  terms  of 
R02,  and  in  the  future  deductions  we  will  always  express  R£,  R32, 
Rn2  in  terms  of  RQ2. 

Make  Rl2  =  aR02    or    a  =  Ri2/R02  ] 
R#=bR02  b  =  R22/R02 

cR02  c  =  R32/R02 


For  convenience  in  future  discussion  we  will  call  a,  b,  c,  n  the  radius 
ratios. 


GUNS.  197 

Now  if  we  divide  numerator  and  denominator  of  each  term  of 
equations  (9),  (10),  and  (11)  by  R02  and  substitute  for  Ri2/R02  its 
value  a  from  equations  (12)  we  obtain 

2  (Po-aPQ        4a(P0-P1)fl02 
^  =  ^  =  3      (a-1)       +   3      (a-1)     7^  <13> 

2  (Pp-aPQ        4a(P0-P1)fl02 
M'-8*-*      (a-1)        •   3      (a-1)     ~? 

2  (Po-aPQ 
^-^  =  -3      (a_i)  ;  (15) 

RULES  FOR  TRANSFORMATION. — We  will  notice  here,  with 
reference  to  the  transformation,  two  facts  on  which  we  will  base 
rules  for  future  transformations.  In  what  follows  we  will  under- 
stand by  the  words  term  factor  a  factor  that  affects  a  whole  term, 
in  contradistinction  to  a  factor  that  affects  a  part  of  a  term  only. 

Comparing  the  first  term  of  the  second  member  of  equation  (13) 
with  the  corresponding  term  of  equation  (9)  we  can  write  the  first 
rule. 

Rule  /.  The  non-appearance  of  R02  in  any  term  involving  the 
radius  ratios  indicates  that  the  term  from  which  it  was  formed 
had  in  the  numerator  the  same  number  of  term  factors  involving 
the  squares  of  the  limiting  radii  as  in  the  denominator. 

In  the  first  term  of  the  second  member  of  equation  (9)  the 
numerator  contains  a  single  term  factor  involving  the  squares  of 
the  radii.  The  denominator  similarly  contains  but  one  such  term 
factor. 

Comparing  the  last  terms  of  equations  (13)  and  (9)  we  see, 

Rule  2.  When  R02  appears  in  the  numerator  of  a  term  involving 
the  radius  ratios,  it  indicates  that  the  original  term  contained  in 
the  numerator  one  more  term  factor  involving  the  squares  of  the 
limiting  radii  than  in  the  denominator. 

Though  the  last  term  of  equation  (13)  contains  in  numerator 
and  denominator  the  same  number  of  term  factors  that  involve 
the  radius  ratios,  the  presence  of  Ro2  in  the  numerator  indicates 
that  the  term  from  which  it  was  formed  had  one  more  such  term 
factor.  That  factor  was  RQ2,  and  since  R02/RQ2  =  1  the  factor  has 
disappeared  from  equation  (13). 


198  ORDNANCE  AND  GUNNERY. 

107.  Stresses  in  a  Simple  Cylinder.  —  In  a  cylinder  forming  a 
part  of  a  gun  we  have  three  cases  to  consider.  There  may  be  a 
pressure  on  the  interior  of  the  cylinder  and  none  on  the  exterior,  the 
atmospheric  pressure  being  considered  zero.  There  may  be  a  pres- 
sure on  the  exterior  of  the  cylinder  and  none  on  the  interior.  Or 
both  exterior  and  interior  pressures  may  be  acting  at  once,  the 
interior  pressure  being  usually  the  greater.  We  will  consider  the 
simple  cylinder  under  these  circumstances. 

Differentiating  equation  (13)  we  obtain 


dSt 

(16) 


dr  3       a-1        r3 

and  differentiating  again, 
d*St 


_ 
dr2  a-1         r 

Similarly  from  equation  (14)  we  obtain 
dS 


p  o-o 


dr       3       a-1    "  r3 
8o(P0-Pi)flo? 


_ 
dr2  a-1        r4 

First  Case.  Interior  Pressure  Only.  —  Making  Pt  =0  in  equa- 
tion (13)  and  remembering  that  r  may  vary  between  the  limits 
#o  and  RI  we  see  that  the  smaller  the  value  of  r  the  greater  will  be 
the  value  of  the  resultant  tangential  stress.  This  is  more  readily 
seen  in  equation  (16)  in  which  the  first  differential  coefficient  of 
the  stress  as  a  function  of  the  radius  is  negative  when  Pi=0, 
showing  that  St  decreases  as  r  increases.  RQ  being  the  least  value 
of  r  the  tangential  stress  is  greatest  at  the  interior  of  the  cylinder. 
Since,  when  PI  =0,  St  in  equation  (13)  is  positive  for  all  values  of 
r,  the  stress  is  one  of  extension  throughout  the  cross  section  of  the 
cylinder.  When  Pi=0  in  equation  (17)  the  second  member  is 
positive,  showing  that  the  curve  of  stress  is  concave  upwards,  the 
axis  of  r  being  taken  as  horizontal.  The  curve  of  tangential  stress 
due  to  an  interior  pressure  only  may  then  be  represented  in  gen- 


GUNS. 


199 


eral  by  the  curve  ti  in  Fig.  39,  the  ordinates  being  the  values  of 
the  stress,  the  abscissas  the  values  of  the  radius. 

The  numbers  at  the  extremities  of  the  curve  are  the  actual 
stresses  due  to  an  interior  pressure  P0  =  36,000  pounds  per  square 
inch  in  a  cylinder  one  caliber  thick.  They  are  calculated  from 
equation  (13)  by  making  PI  =0  and  RI  =  3R0.  When  Ri  =  3R0  we 
have  a  =  Ri2/Ro2  =  9.  The  equation  becomes  with  these  substitu- 
tions 


(20) 


Making  P0  =  36,000  and  r  =  R0  we  obtain  £,  =  57,000;    and  for 


r= 


Similarly  from  equations  (14),  (18),  and  (19)  we  determine  for 
the  radial  stress  produced  by  an  interior  pressure  the  general  curve 


FIG.  39. 


pi,  Fig.  39,  which  shows  radial  compression  throughout  the  cross 
section  with  the  greatest  stress  at  the  interior.  Equations  (14) 
and  (15)  become  for  the  cylinder  one  caliber  thick 


<?      _^o 
«a        12 

and  comparing  these  with  equation  (20)  we  see  that  for  equal 
values  of  r  the  radial  stress  from  an  interior  pressure  is  always  less 


200 


ORDNANCE  AND  GUNNERY. 


than  the  tangential  stress.  The  longitudinal  stress  is  less  than 
either. 

The  radial  stresses  produced  by  a  pressure  P0  =  36,000  are  noted 
on  the  curve  p\. 

We  may  observe  from  equations  (20),  (21),  and  (22)  that  the 
thickness  of  the  cylinder  being  expressed  in  calibers,  or,  what  is  the 
same  thing,  in  terms  of  the  interior  radius,  the  stresses  developed  by 
an  interior  pressure  are  entirely  independent  of  the  caliber,  and 
are  the  same  for  all  cylinders  the  same  number  of  calibers  thick. 

108.  Second  Case.  Exterior  Pressure  Only. — Making  P0  =  0 
in  equations  (13)  to  (19)  we  may  determine  the  curves  of  stress  for 
an  exterior  pressure  acting  alone.  In  this  case  the  value  of  St, 
equation  (13),  is  always  negative.  The  stress  is  therefore  com- 
pressive  throughout  the  cylinder.  dSt/dr,  equation  (16),  is  posi- 
tive. St  therefore  increases  algebraically  with  r.  d?St/dr2,  equa- 
tion (17),  is  negative.  The  curve  is  therefore  concave  downwards. 
The  general  curve  t2,  in  Fig.  40,  therefore  results. 


FIG.  40. 

In  the  same  way  the  general  curve  p^  is  obtained  from  equa- 
tions (14),  (18),  and  (19). 

The  numbers  on  the  curves  are  the  values  for  the  stresses  caused 
by  an  exterior  pressure  Pl  =36,000  Ibs.  on  a  cylinder  one  caliber 
thick,  for  which  Ri=3R0  and  a  =  Ri2/R02  =  9. 

We  see  as  before  that  the  greatest  stresses  are  at  the  interior  of 
the  cylinder,  and  that  the  tangential  stress  is  greater  than  the 
radial.  The  tangential  stress  is  one  of  compression  throughout. 


GUNS. 


201 


The  radial  stress  is  one  of  compression  on  the  exterior  and  of  ex- 
tension on  the  interior. 

109.  Third  Case.     Interior  and  Exterior  Pressures  Acting.— 

The  curves  of  stress  due  to  interior  and  exterior  pressures  acting  at 
once  may  be  found  from  the  equations,  or  by  combination  of  the 
curves  of  stress  due  to  the  pressures  acting  separately.  Thus  in 
Fig.  41,  in  which  the  curves  from  Figs.  39  and  40  are  repeated,  the 
lines  ps  and  ts  represent  the  stresses  due  to  the  equal  interior  and 
exterior  pressures,  P0  =  PI  =  36,000  Ibs. 

The  position  of  the  resultant  curves  of  stress  from  interior  and 
exterior  pressures  acting  together  will,  of  course,  depend  on  the 
relative  values  of  the  two  pressures.  In  Fig.  41  the  pressures  are 


FIG.  41. 

equal.     In  Fig.  42  are  shown  the  curves  resulting  when  the  interior 
pressure  is  twice  the  exterior  pressure;  P0  =  36,000,  PI  =  18,000. 

We  may  see  at  once  from  these  figures  that  the  tangential  re- 
sistance of  a  cylinder  to  an  interior  pressure  may  be  greatly  in- 
creased by  the  application  of  an  exterior  pressure.  Assuming  that 
the  maximum  ordinates  of  the  curves  t\  and  £2,  in  Fig.  41,  are  the 
elastic  limits  6  and  p  respectively,  the  interior  pressure  acting  alone 
would  produce  the  limit  of  tangential  extension.  But  with  the 
exterior  pressure  acting  the  interior  pressure  has  first  to  overcome 
the  existing  compression,  and  as  p  is  usually  greater  than  6  the  in- 
terior pressure  required  to  produce  the  stress  p+d  would  be  more 
than  twice  as  great  as  the  pressure  required  to  produce  the  stress  0 
alone.  That  is  to  say,  that  by  the  application  of  an  exterior  pres- 


202 


ORDNANCE  AND   GUNNERY. 


sure  we  may  more  than  double  the  tangential  resistance  of  a  cylin- 
der to  an  interior  pressure. 

Similarly  it  is  seen  that  the  tangential  resistance  of  a  cylinder 
to  an  exterior  pressure  is  increased  by  the  application  of  an  interior 
pressure. 

no.  Limiting  Interior  Pressures. — In  determining  the  maxi- 
mum safe  pressure  that  can  be  applied  to  the  interior  of  a  cylinder 
there  are  two  cases  to  be  considered;  for,  as  we  have  just  seen,  a 
greater  interior  pressure  may  be  applied  when  there  is  an  exterior 
pressure  acting  than  when  the  interior  pressure  acts  alone. 

INTERIOR  AND  EXTERIOR  PRESSURES  ACTING. — In  Figs.  41  and 
42  we  see  that  when  both  interior  and  exterior  pressures  are  acting 


FIG.  42. 


on  a  given  cylinder  the  maximum  values  of  the  resultant  tangential 
and  radial  stresses  depend  upon  the  relative  values  of  the  pres- 
sures. In  Fig.  41  the  maximum  values  of  the  two  resultant  stresses 
are  equal.  In  Fig.  42  the  resultant  radial  stress  of  compression 
has  a  greater  maximum  value  than  the  resultant  tangential  stress 
of  extension.  Therefore  when  both  pressures  are  acting,  in  order 
to  determine  the  maximum  permissible  interior  pressure  we  must 
find  the  values  of  the  interior  pressures  that  will  produce  the  limit- 
ing stresses  both  of  extension  and  of  compression,  and  then  adopt 
the  smaller  value  as  the  greatest  permissible  pressure.  The  maxi- 
mum stress  in  either  case  occurs  when  r  =  R0.  Therefore  make  this 
substitution  in  equations  (13)  and  (14).  Write  6  for  St  and  —  p  for 
Sp  and  solve  the  equations  for  P0-  The  negative  sign  is  given  to  p, 


GUNS.  203 


since  p  is  an  absolute  value  only,  while  Sp  now  represents  a  stress 
of  compression,  which  is  negative. 


.  3(a-l)p+2aP1 

4a-2 

PO<J  is  the  interior  pressure  that  acting  with  the  exterior  pres- 
sure PI  will  produce  the  limiting  tangential  stress  of  extension  0; 
and  PQp  is  the  interior  pressure  that  acting  with  the  exterior  pres- 
sure PI  will  produce  the  limiting  radial  stress  of  compression  p. 
The  lesser  of  these  two  values  should,  according  to  our  premises, 
always  be  used,  but  it  will  be  seen  later  that  in  practice  it  is  usual 
to  neglect  consideration  of  P0p  and  to  make  use  of  PQe  even  when 
it  is  the  greater.  Assuming  that  0  =  p  we  will  find  by  equating  the 
second  members  of  the  above  equations  that  PQe  will  be  less  than, 
equal  to,  or  greater  than  P0p  as  follows. 

<  < 

PP  QC         /rP    —  3/9  O^\ 

oe  7~  -*  Op     as      °-»  i  TT  i"  v^w 

s>  2* 

in.  INTERIOR  PRESSURE  ONLY. — We  have  seen  in  Fig.  39  that 
the  greatest  stress  from  an  interior  pressure  acting  alone  is  a  tan- 
gential stress  of  extension  at  the  interior  of  the  cylinder.  This 
must  never  exceed  0,  the  elastic  limit  for  extension.  Therefore  to 
find  the  greatest  permissible  value  of  an  interior  pressure  acting 
alone  make  St  =  6  in  equation  (13),  PI  =0,  r  =  R0,  and  solve  for  P0. 

-       3(a-1}o  (26) 


If  the  cylinder  is  one  caliber  thick  RI  =  3R0,  a  =  9,  and 

Poe  =  0.630 
If  the  cylinder  has  infinite  thickness  RI  =  oo  and 

Poe  =  0.756  (27) 

From  which  we  conclude  that  the  greatest  possible  safe  value 
for  an  interior  pressure  acting  alone  in  a  simple  cylinder  is  0.756; 


204  ORDNANCE  AND  GUNNERY. 

and  also  that  comparatively  little  benefit  is  derived  by  increasing 
the  thickness  of  the  cylinder  to  more  than  one  caliber. 

Now  if  we  assume  an  exterior  force  applied  to  the  cylinder  and 
assume  the  effect  of  this  force  to  be  the  stress  p  of  compression, 
the  tangential  stress  that  must  be  produced  by  the  interior  pres- 
sure to  reach  the  limit  of  safety  becomes  p+6,  and  this  being  sub- 
stituted for  6  in  equation  (26)  it  becomes 


From  equations  (26)  and  (28)  the  advantage  derived  by  the 
interior  cooling  of  cast  guns  formed  of  a  single  cylinder  becomes 
apparent.  When  the  gun  is  cooled  from  the  interior  the  layer  of 
metal  immediately  surrounding  the  bore  cools  first  and  contracts. 
The  cooling  and  contraction  of  the  subsequent  layers  then  pro- 
duce a  stress  of  compression  on  the  layers  of  metal  immediately 
surrounding  the  bore  similar  to  the  stress  that  would  be  produced 
by  the  application  of  an  exterior  pressure.  The  limiting  interior 
pressure  in  this  case  would  be  obtained  by  substituting  for  p  in 
equation  (28)  the  value  of  the  stress  resulting  from  the  initial  com- 
pression. 

112.  Graphic  Representation  of  Limiting  Interior  Pressures. 
—  The  system  of  graphics  devised  by  Lieutenant  Commander  Louis 
M.  Nulton,  U.  S.  Navy,  for  the  representation  of  the  relation  be- 
tween the  pressures  and  the  shrinkages  in  cannon  helps  materially 
towards  a  ready  understanding  of  the  subject. 

We  will  begin  the  study  of  the  graphic  system  with  the  repre- 
sentation of  the  limiting  interior  pressures  whose  values  are  given 
by  equations  (23)  and  (24). 

We  will  consider,  as  is  customary  in  gun  construction,  that  6  =  p. 

Equations  (23)  and  (24)  may  be  put  in  the  following  forms,  in 
which  A,  B,  C,  and  D  are  constants  for  any  given  cylinder- 

(23a) 
(24a) 

These  are  the  equations  of  right  lines  that  do  not  pass  through  the 
origin  of  coordinates.     The  lines  may  be  constructed,  as  shown  in 


GUNS. 


205 


Fig.  43,  from  the  axes  of  P0  and  PI,  the  line  marked  PI  Pog  from 
equation  (23a)  and  the  line  PiPo^  from  (24a). 

The  abscissa  of  any  point  of  the  line  P\Poe  is  the  value  of  P0, 
which,  acting  together  with  the  pressure  PI,  whose  value  is  repre- 
sented by  the  ordinate  of  the  point,  will  produce  the  limiting  in- 
terior tangential  stress  of  extension  6.  Similarly  the  abscissa  and 
ordinate  of  any  point  of  the  line  P\P$P  represent  the  pressures 
PO  and  PI  that  acting  together  on  the  cylinder  will  produce  the 
limiting  interior  radial  stress  of  compression  p. 


FIG.  43. 

For  any  given  value  of  either  interior  or  exterior  pressure,  P0 
or  PI,  we  may  at  once  determine  from  the  figure  the  value  of  the 
corresponding  exterior  or  interior  pressure,  PI  or  P0;  that  will 
produce  the  limiting  strain  of  compression  or  of  extension. 

For  Po  =  l#  the  pressure  PI,  whose  value  is  then  \Q ]/a,  see 
equation  (25),  will  produce  in  the  interior  of  the  cylinder  the  maxi- 
mum permissible  stresses  both  of  extension  and  compression. 

The  figure  also  shows  that  the  resistance  of  the  cylinder  to  an 
interior  pressure  is  increased  by  the  application  of  an  exterior  pres- 
sure, since  P0  has  its  least  value  for  PI  =0. 

113.  Limiting  Exterior  Pressure. — This  is  deduced  only  for  the 
case  of  an  exterior  pressure  acting  alone,  as  we  will  have  no  occa- 
sion to  use  the  limiting  values  of  the  exterior  pressure  when  both 
interior  and  exterior  pressures  are  acting. 

From  Fig.  40  we  see  that  the  greatest  stress  from  an  exterior 
pressure  is  a  tangential  stress  of  compression  at  the  interior  of  the 


206  ORDNANCE  AND  GUNNERY. 

cylinder.  This  must  not  exceed  p,  the  elastic  limit  for  compres- 
sion. Therefore  make  St=—p  in  equation  (13),  Po  =  0,  r  =  R0} 
and  solve  for  PI. 

P^°P  (29) 


PIP  being  the  exterior  pressure  that  acting  alone  will  produce 
the  limiting  tangential  stress  of  compression  p. 

For  the  cylinder  one  caliber  thick  Ri=3R0  in  equation  (29), 
a  =  #i2/#o2  =  9,  and 

Pi,  =  0.44^ 

For  the  cylinder  of  infinite  thickness  RI  =  oo  ,  and 


again  showing  how  little  is  gained  by  increasing  the  thickness  of 
the  cylinder  beyond  one  caliber. 

114.  Thickness  of  Cylinder.  —  The  thickness  H  needed  in  a  sim- 
ple cylinder  to  withstand  an  interior  pressure  P0<?  is  obtained  by 
replacing  a  in  equation  (26)  by  its  value  Ri2/R02,  solving  the  equa- 
tion for  RI  and  then  subtracting  R0  from  each  member. 


(30) 


Similarly  the  necessary  thickness  to  withstand  an  exterior  pres- 
sure PI,  is  obtained  from  equation  (29). 


Longitudinal  Strength  of  a  Simple  Closed  Cylinder. — The 
total  pressure  acting  on  each  of  the  end  walls  is  xR02P0.  This 
is  assumed  to  be  uniformly  distributed  over  the  cross  section  of 
the  cylinder,  x(Ri2  —  R02).  The  longitudinal  stress  per  unit  of 
area  is  therefore 

Po 


GUNS.  207 

Substituting  this  value  of  q  in  the  third  equation  (4),  and  for 
t  and  p  their  values  from  (7)  and  (8),  we  obtain  for  the  longitudinal 
stress  in  the  cylinder 


q 


Giving  Elq  its  maximum  value,  0  or  p,  and  solving  for   P0, 
using  6  we  obtain 


for  the  interior  pressure  that  will  produce  the  maximum  permissible 
longitudinal  stress. 
If  Pi=0 

P(w  =  3(a-l)0 

a  value  considerably  greater  than  that  expressed  in  equation  (26). 
Problems.  —  1.  What  is  the  maximum  permissible  interior  pres- 
sure on  a  steel  gun  hoop  the  interior  diameter  of  which  is  20  inches 
and  the  exterior  diameter  28  inches,  the  elastic  limit  of  the  metal 
being  60,000  pounds  per  square  inch? 

Ans.  17,561  Ibs.  per  sq.  in. 

2.  The  steel  tubes  of  a  water  tube  boiler  are  2  inches  in  interior 
diameter  and  2.4  inches  in  exterior  diameter.     The  elastic  limit  of 
the  metal  is  30,000  Ibs.  per  sq.  in.    What  is  the  limiting  interior 
water  pressure?  Ans.  5103.2  Ibs.  per  sq.  in. 

3.  Using  a  factor  of  safety  of  1J,  what  is  the  limiting  interior 
pressure  in  an  air  compressor  tank  with  interior  and  exterior  diam- 
eters of  15  and  17  inches  respectively?    The  elastic  limit  of  the 
metal  is  30,000  Ibs.  per  sq.  in.  Ans.  2391  Ibs.  per  sq.  in. 

4.  An  iron  tube  3  inches  in  interior  diameter  is  subject€d  to 
exterior  pressure,  1326.5  Ibs.  per  sq.  in.    The  elastic  limit  of  the 
metal  is  20,000  Ibs.  per  sq.  in.     What  must  be  the  exterior  diam- 
eter of  the  tube  in  order  that  it  may  safely  withstand  the  pres- 
sure? Ans.  3.25  inches. 

5.  The  6-inch  wire-wound  gun  has  the  following  dimensions  at 
the  powder  chamber:  50  =  4.5  inches,  Ri  =  l2  inches.     If  the  gun 
were  constructed  of  a  single  forging  with  an  elastic  limit  of  60,000 
Ibs.  per  sq.  in.  what  would  be  the  maximum   permissible  powder 
pressure?  Ans.  36,132  Ibs.  per  sq.  in. 

6.  A  boiler  6  feet  in  interior  diameter  is  required  to  withstand 


208  ORDNANCE  AND  GUNNERY. 

a  steam  pressure  of  350  Ibs.  per  sq.  in.  The  elastic  limit  of  the 
metal  is  20,000  Ibs.  per  sq.  in.  What  is  the  maximum  thickness 
required  in  the  shell?  Ans.  0.64  inches. 

7.  The  cylinder  of  a  hydraulic  jack  has  an  interior  diameter  of 
10  inches  and  a  maximum  working  pressure  of  10,000  Ibs.  per  sq. 
in.  The  elastic  limit  of  the  metal  is  40,000  Ibs.  per  sq.  in.  What 
thickness  of  wall  is  required  in  order  that  the  factor  of  safety 
may  be  1£?  Ans.  2.9  inches. 

115.  Compound  Cylinder,  Built-up  Guns. — It  has  been  shown 
that  the  resistance  of  a  cylinder  to  an  interior  pressure  may  be 
greatly  increased  by  the  application  of  pressure  on  the  exterior  of 
the  cylinder.  This  is  accomplished  in  practice  by  shrinking  a 
second  cylinder  over  the  first.  The  shrinkage  causes  a  uniform 
pressure  over  the  exterior  of  the  inner  cylinder  and  an  equal  uni- 
form pressure  on  the  interior  of  the  outer  cylinder. 

The  exterior  pressure  strengthens  the  inner  cylinder  against  an 
interior  pressure,  and  at  the  same  time  weakens  the  outer  cylinder. 

That  the  full  strength  of  the  compound  cylinder  may  be  utilized 
it  is  important  that  the  shrinkage,  and  therefore  the  pressure  at  the 
surfaces  in  contact,  be  so  regulated  that  under  the  action  of  an  in- 
terior pressure  the  interior  of  the  weakened  outer  cylinder  will  not 
be  stretched  to  its  elastic  limit  before  the  inner  cylinder  has  reached 
that  limit.  Otherwise  we  cannot  employ  the  full  strength  of  the 
inner  cylinder.  And  if  the  inner  cylinder  is  strained  to  the  elastic 
limit  before  the  outer  cylinder,  we  cannot  employ  the  full  strength 
of  the  outer  cylinder. 

We  have  seen  in  Fig.  39  that  the  tangential  stress  produced  in  a 
single  cylinder  by  an  interior  pressure  diminishes  in  value  as  the 
thickness  of  the  cylinder  increases.  It  is  therefore  apparent  that 
the  stress  transmitted  to  the  outer  cylinder  may,  by  giving  proper 
thickness  to  the  inner  cylinder,  be  so  reduced  that  when  added  to 
the  initial  stress  existing  in  the  outer  cylinder  this  cylinder  will 
not  be  strained  beyond  its  elastic  limit.  And  by  adjusting  the 
thicknesses  of  the  two  cylinders  and  the  pressure  produced  by  the 
shrinkage,  the  system  may  be  so  constructed  that  the  cylinders 
composing  it  will  both  be  strained  to  the  elastic  limit  at  the 
same  time. 

There  is  evidently  then  a  relation  between  the  thicknesses  of 


GUNS.  209 

the  cylinders  and  the  shrinkage  that  must  be  applied  in  order  that 
the  inner  and  outer  cylinders  shall  be  stretched  to  their  elastic 
limits  by  the  same  interior  pressure.  This  relation  must  be  estab- 
lished if  we  desire  to  utilize  the  full  elastic  strength  of  the  cylinders. 
And  if  a  third  and  a  fourth  cylinder  are  added  the  proper  relation 
between  the  thickness  and  the  shrinkage  must  be  established 
for  these  as  well. 

A  modern  gun  is  built  up  of  a  number  of  cylinders  assembled 
by  shrinkage,  the  number  of  the  cylinders,  from  two  to  four,  de- 
pending upon  the  size  and  power  of  the  gun.  The  shrinkage  of 
each  cylinder  is  so  adjusted  that  under  the  action  of  the  powder 
pressure,  if  the  pressure  becomes  sufficiently  great,  all  the  cylinders 
will  be  strained  to  the  elastic  limit  at  once. 

When  the  powder  pressure  is  acting  in  a  compound  cylinder  the 
system  is  said  to  be  in  action.  When  the  powder  pressure  is  not 
acting  the  system  is  at  rest.  In  action  each  elementary  cylinder 
except  the  outer  one  is  subjected  to  both  interior  and  exterior  pres- 
sures. At  rest  the  inner  cylinder  is  subjected  to  exterior  pressure 
only,  the  outer  cylinder  -to  interior  pressure  only,  and  the  inter- 
mediate cylinders  to  both  pressures. 

1 1 6.  System  Composed  of  Two  Cylinders. — Assume  a  system 
so  assembled  that  under  the  action  of  an  interior  pressure  both 
cylinders  will  be  strained  to  their  elastic  limits. 

Let  RQ,  Ri,  R2,  Fig.  44,  be  the  radii  of  the  successive  surfaces 

from  the  interior  outwards, 
P0,  -Pi,  PZ,  the  normal  pres- 
sures on  the  successive  sur- 
faces when  the  system  is  in 
action, 

PO,  Pi,  P2,  variations  in  P0,  PI, 
P2,  as  the  system  passes 
from  a  state  of  action  to  a 
state  of  rest, 

00,  #i,  the  tensile  elastic  limits 
of  the  inner  and  outer  cyl- 
inders respectively, 

po,  pi,  the  compressive  elastic  FIG.  44. 

limits, 


210  ORDNANCE  AND  GUNNERY. 

E,  the  modulus  of  elasticity,  assumed  the  same  for  both 

cylinders, 
PI,,  the  normal  pressure  at  the  surface  of  contact  when 

the  system  is  at  rest. 

Application  of  Formulas  to  Outer  Cylinders.  —  It  will  be  well, 
before  proceeding  further,  to  show  how  the  formulas  deduced  for 
a  single  cylinder  are  made  applicable  to  outer  cylinders  in  com- 
pound systems. 

Thus  equation  (23) 


4a+2 


gives  the  value  of  the  limiting  pressure  in  a  single  cylinder  when 
the  pressure  PI  acts  on  the  exterior. 

Let  us  make  this  apply  to  the  second  cylinder  of  a  compound 
system. 

Substituting  for  a  its  value  Ri2/R02  and  clearing  of  fractions  in 
numerator  and  denominator, 


W  +  2R02 

Now  to  apply  this  equation  to  the  second  cylinder  change  all 
zero  subscripts  to  1,  and  subscripts  1  to  2.  Making  these  changes, 
dividing  numerator  and  denominator  by  R02,  we  obtain,  since 
R^/Ro*  =  a  and  R22/R02  =  b, 


Comparing  this  equation  with  (31),  from  which  it  has  been  de- 
duced, we  see  that  the  transformation  may  be  immediately  made 
by  substituting  6  for  a,  and  by  writing  a  after  the  numerical  quan.- 
tities  that  are  affected  when  we  substitute  Ri2/R02  for  a  and  clear 
of  fractions. 

We  have  made  this  transformation  under  transformation  rule 
1,  page  197.  In  equation  (31)  the  numerator  forms  but  one  term 
factor  and  the  denominator  another.  As  Ro2  does  not  appear  in 


GUNS.  211 

(31)  we  know  that  the  equation  from  which  it  is  derived,  equation 
(32),  is  of  the  same  form. 

The  following  equation,  which  refers  to  pressures  in  the  inner 
cylinder  of  a  compound  system, 

(6—  a)  a(c-6) 

P1  =  °    b€COmes    P2  =  pl 


for  the  second  cylinder,  since  the  absence  of  R02  in  the  first  equa- 
tion indicates  that  its  original  equation  had  two  term  factors  in- 
volving the  squares  of  the  radii  in  the  numerator  as  well  as  in  the 
denominator.  Therefore  consider  1  =  R02/Ro2  as  present  as  a 
term  factor  in  the  numerator  of  the  first  equation,  change  to 
Ri2/Ro2,  and  write  a  for  this  quantity  in  the  second  equation. 
The  equation 


becomes,  if  made  applicable  to  the  second  cylinder, 

fu__8(6-c)ft  +  2fcP.  (35) 

since  the  absence  of  R02  indicates  that  the  original  equation  had 
one  term  factor  in  the  denominator  as  well  as  in  the  numerator. 
Equation  (13)  is,  for  the  first  cylinder, 

Elt=StJ(£^  + 


and  becomes  for  the  second  cylinder 

2(aP1-6P2) 
El<=S<=     3(b-a)  3(6-a)     ~^~ 

Under  transformation  rule  2  the  presence  of  R02  in  the  nu- 
merator of  the  last  term  indicates  that  the  original  term  had  two 
term  factors  involving  the  squares  of  the  limiting  radii  in  the 
numerator  and  one  in  the  denominator.  Therefore  supply  the 
missing  factor  1  =  R02/R02,  change  to  R^/Ro2,  write  a  in  (36)  for 


212  ORDNANCE  AND  GUNNERY. 

this  quantity  and  change  the  a  in  (13)  to  b.  R02  is  itself  not 
affected  in  the  transformation,  as  in  reality  it  disappears  during 
the  transformation  and  reappears  later  by  reinsertion. 

Whenever  in  doubt  as  to  a  transformation  replace  the  radius 
ratios  by  their  values,  clear  the  resulting  fractions,  make  the  trans- 
formation, and  rewrite  the  ratios. 

117.  System  in  Action.  —  When  the  system  is  in  action  the 
outer  cylinder  is  strained  to  its  elastic  limit  by  an  interior 
pressure.  The  limiting  pressure  is  given  by  equation  (26),  changing 
the  subscripts  to  conform  to  the  nomenclature  above. 

3(6-a) 
Fl'~  46  +  2/1 

The  pressure  Pig  will  extend  the  inner  layer  of  the  outer  cylin- 
der to  its  elastic  limit.  It  is  therefore  the  greatest  safe  pressure 
that  can  be  applied  to  the  interior  of  this  cylinder. 

The  pressure  P\6  just  found  also  acts  upon  the  exterior  of  the 
inner  cylinder,  and  the  pressure  P0  upon  the  interior.  For  the 
limiting  values  of  the  interior  pressure  we  'have,  under  these  cir- 
cumstances, from  equations  (23)  and  (24), 


4a+2 

3(a-lVo4-2aPlg 
4a-2 


The  smaller  of  these  values  as  determined  by  the  test,  equation 
(25),  must  be  used  as  the  limiting  interior  pressure.  Acting  with 
the  pressure  Pig  it  brings  the  inner  layer  of  the  inner  cylinder  to 
its  elastic  limit  of  tension  or  compression  according  as  P0<?  or  P0p 
is  the  less.  At  the  same  time  the  pressure  P\g  stretches  the  inner 
layer  of  the  outer  cylinder  to  its  elastic  limit. 

Equation  (37),  containing  in  the  second  member  known  quan- 
tities only,  is  solved  first,  and  the  value  of  P^g  obtained  is  sub- 
stituted in  equation  (38)  or  (39)  as  determined  by  the  test.  The 
maximum  permissible  value  of  P0  results. 


GUNS.  213 

1 1 8.  System  at  Rest. — We  have  seen  in  Figs.  40  and  41  that  an 
exterior  pressure  acting  alone  on  a  cylinder  may  produce  a  greater 
stress  than  when  an  interior  pressure  is  also  acting. 

It  may  be,  therefore,  that  the  pressure  Pig  deduced  as  a  safe 
pressure  for  the  system  in  action  may  produce  a  higher  pressure 
than  the  inner  cylinder  can  safely  withstand  v.hen  the  system  is 
at  rest,  that  is,  when  the  interior  pressure  P0  is  zero.  This  must 
be  determined  before  we  can  assume,  as  safe  values  for  the  pres- 
sures, the  values  obtained  from  the  consideration  of  the  system  in 
action. 

As  the  system  passes  from  a  state  of  action  to  a  state  of  rest 
variations  occur  in  the  pressures  acting,  and  consequent  variations 
in  the  stresses  at  the  various  surfaces.  p0  and  pi  represent  the 
variations  in  the  pressures  PO  and  PI  respectively.  Since  the  in- 
terior pressure  changes  from  P0  to  0  we  have 

Po=-Po  (40) 

because  P0— Po  =  0;  that  is,  the  algebraic  sum  of  the  pressure  in 
action  and  the  variation  in  the  pressure  is  the  pressure  at  rest. 

The  variations  in  the  tangential  stresses  due  to  the  variations 
in  the  pressures  may  be  determined  from  equation  (13).  For  the 
exterior  of  the  inner  cylinder,  the  pressures  —  PO  and  pi  acting, 
write  —  P0  for  P0,  p\  for  PI  and  make  r  =  Ri. 

It  will  be  noticed  that  when  r  =  R±  in  equations  (13)  and  (14) 
the  last  factor  becomes  R02/Ri2  or  I/a,  which  cancels  the  a  in  the 
numerator  of  the  last  term. 

-6Po-(2a+4)yi 
— 3(a— 1) 

For  the  outer  cylinder  equation  (13)  takes  the  form  of  equa- 
tion (36).  For  the  interior  of  the  outer  cylinder,  the  pressure 
pi  acting  alone,  write  p:  for  PI,  make  P2  =  0,  and  r  =  Ri. 

(2a+46)Pl 
8t       3(6-a) 

As  the  surfaces  of  contact  of  the  two  cylinders  form  virtually 
one  surface  the  two  values  for  the  variation  in  the  stress  at  this 


214  ORDNANCE  AND  GUNNERY. 

surface  must  be  equal.    Equating  the  second  members  of  equa- 
tions (41)  and  (42)  and  solving  for  pi,  we  obtain 

(b-a)P0  „„. 

pl=  -fiW 

which  expresses  the  relation  between  the  variations  in  pressure  at 
the  interior  and  exterior  of  the  inner  cylinder. 

We  have  designated  the  pressure  at  the  surface  of  contact  of 
the  two  cylinders,  system  at  rest,  by  PI«.  The  variation  in  pres- 
sure from  the  state  of  action  to  the  state  of  rest  must  therefore  be 

pi=-(Pi*-Pis)=Pi8-Pi*  (44) 

because  Ple-  (Pi,-Pi.)  =Pi..     Solving  (44)  for  Plt 


and  substituting  the  value  of  p\  from  equation  (43)  we  obtain 

(6-q)Po 


for  the  value  of  the  pressure  on  the  exterior  of  the  inner  cylinder, 
system  at  rest. 

119.  This  value  of  Pl4  must  not  exceed  the  maximum  permis- 
sible value  of  an  exterior  pressure  acting  alone  on  the  inner  cyl- 
inder, as  given  by  equation  (29). 


If  it  does  the  inner  cylinder  at  rest  will  be  crushed  by  the  pressure 
applied  to  strengthen  it  in  action. 

The  condition  that  Pi8  shall  not  exceed  P\p  may  be  expressed 
/ 

(6-q)P0       o-l 
P*'-P»-  0(6_1)          2a    po  " 

If  the  values  of  Plg  from  equation  (37)  and  of  P0  from  (38)  or 
(39)  do  not  fulfill  the  above  conditions  these  values  for  the  pressures 
cannot  be  used  for  the  system  in  action. 


GUNS.  215 


To  find  the  safe  values  for  the  pressures  in  this  case  we  must 
reduce  the  value  of  the  first  member  of  (47),  P\s,  until  it  is  equal 
to  the  second  member,  Plp.  Plfl  becomes  then  PI  and  we  have 


This  is  the  relation  that  must  exist  between  PI  and  P0  in  order 
that  these  pressures  may  be  safe  for  the  system  at  rest. 

Equations  (38)  and  (39)  express  the  relations  between  the  safe 
pressures  for  the  system  in  action. 

If  therefore  we  substitute  the  lesser  value,  PI  from  (48),  forP19 
in  equations  (38)  and  (39)  and  solve  for  P0  we  will  obtain  the 
values  of  P0  that  will  be  safe  both  in  action  and  at  rest. 


-  lf 


The  lesser  of  these  two  values  will  be  the  limiting  safe  interior 
pressure  that  can  be  applied  to  the  system. 

Assuming  6  and  p  equal,  we  will  find  by  equating  the  second 
members  of  equations  (49)  and  (50)  that  PQO  will  be  less  than, 
equal  to,  or  greater  than  P0p  according  as 


(51) 


120.  Graphic  Representation.  System  at  Rest  and  in  Ac- 
tion. —  Equation  (43)  expresses  the  value  of  the  variation  pi  in  the 
exterior  pressure  for  a  variation  P0  in  the  interior  pressure.  Drop- 
ping the  negative  sign  for  convenience  this  equation  may  be 
written,  for  a  given  cylinder, 


216 


ORDNANCE  AND  GUNNERY. 


and  may  be  represented  by  the  line  piP0  in  Fig.  45.  The  variation 
in  exterior  pressure  increases  directly  with  the  interior  pressure  at 
a  rate  represented  by  the  inclination  of  the  line  p\Po. 

The  lines  p\Pog  and  P\PQP  represent,  as  in  Fig.  43,  the  coordi- 
nate limiting  pressures  for  the  inner  cylinder.  Plfl  is  the  limiting 
pressure  at  the  surface  of  contact  in  action  obtained  from  equation 
(37).  Considering  only  the  tangential  stresses,  the  abscissa  of  the 
point  c,  P0  =  42,955,  is  the  limiting  value  of  the  interior  pressure  in 
action.  As  the  system  passes  from  action  to  rest  the  exterior 
pressure  falls  at  the  rate  represented  by  the  inclination  of  the  line 


19911  28969 

FIG.  45. 


42956 


P\PQ.  Therefore  drawing  through  c  a  line  parallel  to  piPo,  the 
point  where  it  cuts  the  axis  PI  will  be  the  value  of  Pi8,  the  pres- 
sure at  rest,  P0  being  zero  at  this  point.  If  the  value  of  P\s  is 
less  than  Plpf  the  limiting  value  of  the  pressure  at  rest  calculated 
from  equation  (46),  the  value  Plff  is  a  safe  value.  If  PIS  is 
greater  than  Pip  we  cannot  use  P\e  in  action.  In  this  case  we 
would  find  the  permissible  value  of  PI  in  action  by  drawing  a  line 
from  PIP  parallel  to  p\P0.  Its  intersection  with  PiPoe  would  give 
the  values  of  the  coordinate  limiting  exterior  and  interior  pres- 
sures in  action. 

121.  Maximum  Value  of  the  Safe  Interior  Pressure  in  a 
Compound  Cylinder. — The  stresses  and  strains  produced  by  any 
pressure  applied  to  a  compound  cylinder  are  exactly  the  same  as 
would  be  produced  by  the  same  pressure  applied  to  a  single  cyl- 
inder of  the  same  dimensions. 


GUNS.  217 

The  resultant  stresses  in  the  compound  cylinder  are  the  alge- 
braic sums  of  the  stresses  already  existing  in  the  cylinder  and 
those  induced  by  the  application  of  the  pressure,  and  similarly  for 
the  strains. 

As  the  resultant  stresses  may  never  exceed  the  elastic  limits  of 
extension  and  compression,  the  maximum  permissible  pressure  in 
any  cylinder  is  given  by  equation  (28). 

Changing  a  into  b  to  make  of  the  compound  cylinder  a  single 
cylinder  whose  outer  radius  is  R2,  we  have 

3(6-1) 


Making  R2  =  <x>,  and  therefore  b  =  R22/Ro2  =  <*>,  we  obtain 


which  is  the  greatest  possible  value  of  the  safe  interior  pressure  in 
a  compound  cylinder. 

The  same  result  is  obtained  by  substituting  60+  p0  for  6  in 
equation  (27). 

122.  Shrinkage.  —  The  absolute  shrinkage  is  the  difference  be- 
tween the  exterior  diameter  of  the  inner  cylinder  and  the  interior 
diameter  of  the  outer  cylinder  before 
heated  for  assembling,  lab,  Fig.  46. 

The  relative  shrinkage  is  the  absolute 
shrinkage  divided  by  the  diameter,  or 
the  shrinkage  per  unit  of  length,  ab/Ri. 
The  shrinkages  are  so  small  that  it  is 
innecessary  to  distinguish  between  the 

lengths  of  the  radii  as  affected  bv  the 
.    .  ,  FIG.  46. 

shrinkage. 

The  shrinkage  diminishes  the  exterior  radius  of  the  inner  cyl- 
inder, when  cold,  and  increases  the  interior  radius  of  the  outer  cyl- 
inder, so  that  the  radius  R\  of  the  surfaces  in  contact  is  of  a  length 
intermediate  between  the  lengths  of  the  original  radii. 

The  relative  shrinkage  is,  Fig.  46, 


(52) 


218  ORDNANCE  AND  GUNNERY. 

The  relative  compression  ci/Ri  is  the  strain  per  unit  of  length 
produced  by  the  pressure  PI«  acting  on  the  exterior  of  the  inner 
cylinder.  As  the  circumference  is  proportional  to  the  radius  the 
diminution  of  the  circumference  per  unit  of  length  will  be  the  same 
as  the  unit  shortening  of  the  radius,  and  the  value  of  the  tangential 
strain  produced  by  the  pressure  PI,  may  be  obtained  from  equa- 
tion (13),  by  making  P0  =  0.and  r  =  Ri. 

(2a+4)Plg 
lt  =  3E(a_l} 

The  negative  sign  is  omitted,  as  it  simply  indicates  compression. 

The  tangential  strain  co/R\  at  the  interior  of  the  outer  cylinder 
is  similarly  obtained  from  equation  (13),  which  for  the  second  cyl- 
inder takes  the  form  of  equation  (36).  Making  P\  =  P\t,  P2  =  0, 
and  r=Ri, 

(2a+46)Plg 


Therefore  from  equation  (52)  we  have  for  the  relative  shrinkage 

2a(6-l)P1< 
g>~E(a-l)(b-a) 

The  absolute  shrinkage  is 

-it 


The  exterior  diameter  of  the  inner  cylinder  before  shrinkage 
should  be 

(55) 


RI  representing  here  the  interior  radius  of  the  outer  cylinder 
before  assembling. 

The  relative  tangential  compression  of  the  bore  due  to  the 
shrinkage  pressure  Ple  is  found  from  equation  (13)  by  making 
Po-0,  PI=PI,,  and  r  =  R0. 


E(a-l] 


GUNS.  219 

Substituting  the  value  of  P^  from  equation  (54)  and  reducing 
we  have 

- 


from  which  we  may  obtain  at  once  the  tangential  compression  when 
the  absolute  shrinkage  is  known. 

Since,  equation  (13),  Elt  =  St  the  tangential  stress  on  the  bore 
in  pounds  per  square  inch  is  found  by  multiplying  the  relative  com- 
pression by  the  modulus  of  elasticity;  30,000,000  for  gun  steel. 

123.  GRAPHIC  SHRINKAGE.—  Equation  (54)  becomes  for  a  given 
compound  cylinder 


It  is  represented  in  Fig.  45  by  the  line  SiPi8,  the  axis  of  Si  coin- 
ciding with  the  axis  of  P0.  Different  scales  are  used  on  these 
two  axes.  The  coordinates  of  any  point  of  the  line  *SiPi8  repre- 
sent, for  the  given  compound  cylinder,  absolute  shrinkage  and 
the  pressure  produced  by  it  at  the  surface  of  contact.  Therefore 
to  find  the  shrinkage  necessary  to  produce  the  required  pressure 
at  rest,  Pi8,  draw  the  horizontal  line  from  Pi8  and  the  vertical 
line  from  its  intersection  with  SiPis.  The  intercept  on  the  axis 
of  Si  is  the  value  of  the  absolute  shrinkage  that  will  produce  the 
pressure  Pi8.  Si  =0.0085  in  the  case  illustrated. 

124.  Radial  Compression  of  the  Tube. — The  value  of  the 
pressure  on  the  exterior  of  the  inner  cylinder  at  rest  is  given  by 
equation  (45), 

(&-a)Po 


It  will  be  seen  from  this  equation  that  the  larger  the  value  of 
PO  used  the  less  will  be  the  value  of  PIS;  and  from  equation  (54) 
we  see  that  the  less  the  value  of  P\8  the  less  will  be  the  shrinkage. 
Therefore  if  when  P0g  is  greater  than  P0p  we  use  PQg  in  equa- 
tion (45),  the  resulting  shrinkage  will  be  less  than  if  P0p  were 
used,  and  as  may  be  shown  by  equation  (14)  the  resulting  radial 
stress  at  the  inner  surface  of  the  inner  cylinder,  system  in  action, 
will  be  increased.  Now  in  deducing  the  value  for  the  shrinkage 
we  have  used  the  pressures  calculated  to  strain  the  metal  to 


220  ORDNANCE  AND  GUNNERY. 

its  elastic  limit.  Therefore  with  reduced  shrinkage  the  pressure 
PQp  will  produce  a  stress  of  radial  compression  at  the  inner  sur- 
face of  the  tube  greater  than  the  elastic  limit  of  the  metal. 

But  it  is  found  that  the  metal  of  the  inner  cylinder  supported 
as  it  is  by  the  outer  cylinder  has  greater  strength  to  resist  radial 
compression  than  is  indicated  by  the  tests  of  the  detached  speci- 
mens of  the  metal  used  in  determining  the  elastic  limits;  and 
as  the  reduced  shrinkage  resulting  from  the  use  of  Pog  in  equa- 
tion (45)  reduces  all  the  stresses  on  the  system  in  a  state  of  rest, 
and  those  on  the  outer  cylinder  in  a  state  of  action,  it  is  the  prac- 
tice to  use  Pog  instead  of  P0p  in  calculating  the  shrinkage. 

Guns  as  constructed  yield  by  tangential  extension,  and  the 
radial  over-compression  if  it  exists  does  not  determine  rupture. 
Consequently  the  tangential  elastic  resistance  of  the  gun,  even 
though  frequently  greater  than  the  radial  elastic  resistance,  is 
taken  as  the  elastic  strength  of  the  gun. 

125.  Prescribed  Shrinkage. — Equation  (54)  expresses  the  re- 
lation between  the  shrinkage  and  the  pressure  that  it  produces. 
When  for  any  reason  the  compound  cylinder  is  not  assembled 
in  such  a  manner  as  to  offer  the  maximum  elastic  resistance, 
as,  for  instance,  when  a  certain  shrinkage  less  than  the  maximum 
permissible  shrinkage  is  prescribed,  the  pressure  due  to  the  pre- 
scribed shrinkage  may  be  found  by  solving  equation   (54)   for 
Pi8.     The  elastic  resistance  of  the  compound  cylinder  assembled 
with  the  prescribed  shrinkage  will  then  be  found  from  equations 
(49)  and  (50)  by  substituting  for  PIP,  which  represents  the  pressure 
at  rest,  the  value  of  PIS  from  equation  (54),  which  is  the  actual 
pressure  applied. 

The  prescribed  value  of  S\  will  give  in  equation  (56)  the  re- 
sulting relative  tangential  compression  of  the  bore. 

GRAPHIC  REPRESENTATION. — In  Fig.  45  let  the  point  0.008 
be  the  value  of  the  prescribed  shrinkage.  By  following  the  broken 
lines  from  this  point  we  find  on  the  axis  PI  the  resulting  pressure 
at  the  surface  of  contact,  system  at  rest;  and  at  6  on  the  line 
PiPoe  the  point  whose  coordinates  are  the  limiting  interior  and 
exterior  pressures,  system  in  action. 

126.  Application  of   the  Formulas. — Assuming  the  caliber 
of  the  bore  and  the  thicknesses  of  the  cylinders,  to  determine 


GUNS.  221 

the  shrinkage  and  the  permissible  pressures  in   the  compound 
cylinder  assembled  to  offer  the  maximum  resistance. 

The  formulas  usually  required  for  a  system  composed  of  two 
cylinders  are  here  assembled  for  convenience. 


(12) 

3(6-a) 


3(0-1)^0 


6  —  a 


4a-2 


.  p        (b-a}Po*  -  a-l 

•"      **•          «^_1N      <      O/T    rO      ^Ip  ^t<; 


^     ' 


2(P0-oPi)      4a(P0-P1)  7g02 
3o-l  3o-l        r2 


4a(P0-P1)  ^ 
-  2 


222  ORDNANCE  AND  GUNNERY. 

In  equation  (43)  above,  —  PO  has  been  replaced  by  its  value 
PQ  from  equation  (40)  in  order  to  make  the  equation  general. 
—  P0  is  a  particular  value  of  p0. 

In  the  first  member  of  (47)  Poe  is  written  for  P0  to  make  the 
equation  conform  to  the  practice  of  using  P0ff  in  determining  the 
shrinkage. 

PROCESS.  —  Use  the  values  of  6  and  p  determined  in  the  testing 
machine. 

Find  Pig  from  equation  (37). 

Find  PQO  and  P0p  from  (38)  and  (39). 

Make  the  test  indicated  in  (47)  and  if  either  of  the  conditions 
are  met  use  the  value  of  the  first  member  of  (47)  for  Pl8  in  (54) 
and  find  Si. 

The  values  already  found  for  Pi9  and  P09  are  then  the  limit- 
ing safe  pressures. 

If  the  first  member  of  (47)  is  greater  than  the  second, 
Find  PO*  and  P0p  from  (49)  and  (50). 
Use  Pi,  from  (47)  for  PI.  in  (54)  to  find  Si. 

The  stresses  and  strains  produced  by  any  pressures  are  found 
by  means  of  equations  (13)  and  (14);  the  tangential  stresses  and 
strains  from  equation  (13),  the  radial  from  equation  (14). 

127.  Problem  i.  —  The  dimensions  of  the  4.7  inch  siege  rifle,  at 
the  section  marked  IV  in  Fig.  47,  are: 

#o  =  2.35  inches,  #i  =  3.86,  722  =  6.  The  prescribed  elastic 
limit  for  both  tube  and  jacket  is  50,000  Ibs.  per  sq.  in.  What 
will  be  the  shrinkage  when  the  cylinders  are  assembled  to  offer 
the  maximum  resistance,  and  what  will  be  the  maximum  per- 
missible interior  pressure? 

We  have  a  =  Ri2/R02  =  2.698 

b  =  R22/R02  =  6.5187 
b-  a  =  3.8207 


Equation  (37)     Pw-  -  50000  -  18210 


3X1.698  X  50000  +  6  X  2.698x18210 
06  =  12  792  =42956 


GUNS.  223 

(39)          Po^ 


_4X3.86X2.698X  5.5187  X7187 
30,000,000  X  1  .698  X  3.8207 

The  outer  diameter  of  the  tube  must  therefore  be  0.0085 
inches  greater  than  the  inner  diameter  of  the  jacket  before 
assembling. 

If  P0p  were  used  in  place  of  P0g  in  the  determination  of  P18, 
equation  (47),  we  would  obtain  Pls  =  7909,  and  from  (54)  Si  = 
0.00934. 

128.  GRAPHIC   SOLUTION.  —  In  Fig.  45  is  shown  the  graphic 
solution  of   Problem   1.     For   this  problem  the  equations   take 
form  as  follows. 

(38)  Poe  =  19910  +  1.325Pi 

(39)  P0,  =  28968  +0.614P! 
(43)  pi=0.2566P0 

(47)  £!=0.0000118P18 

These  equations  are  represented  by  the  lines  of  the  figure 
drawn  to  scale.  Determine  from  equation  (37)  the  limiting 
interior  pressure  on  the  jacket,  PIQ.  From  this  point  on  the 
axis  of  PI  draw  the  horizontal  line.  It  cuts  PiPog  at  the  point  c, 
for  which  P0  =  42956.  Passing  from  action  to  rest  the  pressure 
P!  varies  at  the  rate  indicated  by  the  inclination  of  the  line  p\PQ. 
Therefore  draw  from  c  a  line  parallel  to  this  line.  It  cuts  the 
axis  of  PI  at  Pis,  which  is  the  pressure  at  rest.  PI,  is  less  than 
PIP,  equation  (47),  also  represented  in  the  figure.  Therefore  Pu 
in  action  is  a  safe  pressure.  Drawing  the  horizontal  line  from 
Pis  and  the  vertical  line  from  its  point  of  intersection  with  S\Pi8 
we  find  that  the  absolute  shrinkage  that  will  produce  the  pressure 
P18  is  &  =  0.0085. 

129.  Problem  2.  —  What  are  the  stresses  on  the  inner  and 
outer  surfaces  of  the  tube  of  the  gun  in  the  last  problem,  both 


224  ORDNANCE  AND  GUNNERY. 

at  rest  and  in  action,  assuming  the  gun  to  be  assembled  with  the 
shrinkage  determined  in  that  problem,  and  using  the  pressure 
P0p  =  40146,  equation  (39),  as  the  interior  pressure  in  action? 

The  pressure  at  rest,  Pi«  =  7187,  determined  in  Problem  1, 
acts  alone. 

Tangential  stresses,  (13),  St(Ro)  =  -22839     St(Ri)  =  - 13257 
Radial  stresses,  (14),         SP(R0)  =  +  7613       Sp(fli)  =  - 1970 

In  Problem  1  in  determining  by  equation  (47)  the  pressure  at 
rest  we  used  Poe  =  42956  Ibs.  as  the  pressure  in  action.  The 
pressure  at  the  outer  surface  of  the  tube  in  action  as  given  by 
equation  (37),  P\9  =  18210,  will  therefore  be  produced  only  by 
the  interior  pressure  P00-  An  interior  pressure  PQP  =  40146  Ibs., 
less  than  P06,  will  produce  a  pressure  on  the  exterior  of  the  tube 
less  than  18210  Ibs.  Equation  (43)  gives  the  value  of  the  variation 
in  the  exterior  pressure  due  to  any  variation  pQ  in  the  interior 
pressure.  Making  p0  =  42956  -40146  =  2810  in  equation  (43)  we 
find  pi  =  721.  The  pressure  PI  in  action,  due  to  the  interior 
pressure  P0,,  is  therefore  18210-721  =  17489  Ibs. 

Making  P0  =  40146  and  PI  =  17489  we  find 

Tangential  stresses,  (13),    St(R0)  =  +  45236    St(Ri)  =  +  15027 
Radial  stresses,  (14),          SP(R0)  =  -50764    Sp(Ri)  =  -20555 

Had  the  shrinkage  in  Problem  1  been  determined  by  the  use 
of  PQP  =  40146  in  equation  (47),  that  pressure  in  action  would 
have  compressed  the  inner  layer  of  the  tube  radially  to  its  elastic 
limit,  50000  Ibs.  But  with  the  reduced  shrinkage  due  to  the  use 
of  Poe  in  equation  (47)  the  pressure  of  40146  Ibs.  exerts  a  radial 
stress  on  the  inner  layer  of  the  tube  of  50764  Ibs.,  which  is  in  excess 
of  the  elastic  limit. 

130.  GRAPHICALLY. — The  pressure  PI  in  action,  used  in  deter- 
mining the  stresses  from  equations  (13)  and  (14),  may  be  ob- 
tained from  Fig.  45.  The  shrinkage  being  0.0085,  Pl8  is  the 
pressure  at  rest.  From  Pl8  follow  the  line  of  variation  in  pressure 
to  the  point  a,  whose  abscissa  is  P0/0  =  40146.  The  ordinate  of 
this  point  is  the  pressure  PI  in  action  when  P0  =  40146.  There- 
fore PI  =17489. 


GUNS.  225 

131.  Problem  3.  —  The  shrinkage  actually  prescribed  at  the 
section  of  the  4.7  inch  rifle  used  in  Problem  1  is  0.008  of  an  inch. 
What  is  the  elastic  resistance  of  the  gun,  tangential  and  radial, 
at  the  section,  and  what  is  the  relative  compression  of  the  bore 
and  the  stress  of  tangential  compression  at  the  surface  of  the 
bore? 

_  0.008  X  30,000,000  X  1  .698  X  3.8207 
19  ~          4X3.86X2.698X5.5187 

3X1.698X50000  +  6X2.698X6773 
(49)          P09=-         -  OQA  -  =  42178 

12702 
\o\j)         *op— 


5.5187 
3X1.698X50000+2X2.698X6773 


Q  QOH7 

R702-2 

^5.5187 


(13)  St  =  Elt 

132.  GRAPHICALLY.  —  From  the  point  0.008,  Fig.  45,  on  the 
axis  of  Si  follow  the  broken  lines  and  obtain  successively  the  values 
found  above  for  PI,,  P0p,  and  Pog. 

133.  Curves  of  Elastic  Resistance.  —  In  the  same  way  the 
elastic  resistances  are  found  at  various  sections  of  the  gun,  and 
the  curves  of  elastic  resistance  shown  in  Fig.  47  are  constructed. 
By  comparing  the  ordinates  of  these  curves  with  the  corresponding 
ordinates  of  the  curve  of  powder  pressures  it  will  be  seen  that 
the  gun  has  a  factor  of  safety  of  about  1J  over  the  part  of  its 
length  that  is  subjected  to  the  maximum  pressure. 

Problem  4.  —  What  will  be  the  tangential  stresses  in  the  system 
assembled  as  in  Problem  3  under  a  powder  pressure  of  32,000  Ibs. 

per  sq.  in.  ? 

#o  =  2.35      #i  =  3.86      #2  =  6     (See  Problem  1) 

The  pressure  at  rest,  Pi8  =  6773,   determined  in  Problem  3, 
produces  stresses  as  follows,  equations  (13)  and  (36). 

Tube,     (13),  St(R0)  =  -21523        St(Ri)  =  -12493 
Jacket,  (36),  St(R0)  =  +  18596       -St(Ri)  =  +  9566 


SOI 


SCALE  OF  ELASTIC  RESISTANCE- 1000  LBS.  PER  SO.  IN. 


SCAU  OF  ttl.  COMMISSIONS 
TCN    THOUSANDTHS 


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GUNS.  227 

The  stresses  within  the  elastic  limit  produced  by  an  interior 
or  exterior  pressure  on  a  compound  cylinder  are  exactly  the  same 
as  would  be  produced  by  the  same  pressure  on  a  simple  cylinder 
of  the  same  dimensions.  If  therefore  we  consider  the  gun  as  a 
simple  cylinder  and  calculate  the  stresses  due  to  an  interior  pressure 
of  32,000  Ibs.,  these  stresses  will  be  the  variations  in  the  stresses 
in  the  compound  cylinder  as  it  passes  from  rest  to  action,  and  the 
algebraic  sums  of  the  stresses  at  rest  and  the  variations  will  be  the 
stresses  in  action. 

Considering  the  gun  as  a  simple  cylinder  acted  on  only  by  the 
interior  pressure,  32,000  Ibs.,  we  obtain  from  equation  (13)  for 
the  stresses  at  the  surfaces  for  which  r  =  -R0  =  2.3o,  r  =  3.86,  and 
r  =  #!=6: 

Inner  surface  of  cylinder,   St  =  +  54265 
At  r  =  3.86,  £«=+ 22546 

Outer  surface  of  cylinder,    St  =  + 11597 

Taking  the  algebraic  sums  of  these  stresses  and  those  above 
determined  for  the  system  at  rest,  we  find  for  the  stresses  in  action: 

Tube,    St(R0)=  +32742,     St(Ri)  =  +  10053 
Jacket,  St(R0)  =  +41142,     St(Ri)  =  +21163 

134.  GRAPHICALLY. — As  in  the  graphic  solution  of  Problem  2, 
the  pressure  PI  corresponding  to  the  interior  pressure  P0  =  32,000 
is  found  from  Fig.  45  by  following  the  line  of  variation  of  pressure 
for  Pu  =  6773  to  the  point  d  whose  abscissa  is  P0  =  32,000.     The 
ordinate  of  this  point  is  PI,  and  this  being  substituted  with  P0 
in  equations  (13)  and  (14),  the  values  of  the  stresses  are  derived. 

135.  Curves  of  Stress  in  Section. — The  curves  of  tangential 
stress  in  a  section  of  a  gun  composed  of  two  cylinders  assembled 
to  offer  the  maximum  resistance  are  shown  in  Fig.  48.     The  curves 
s  show  the  stresses  in  the  cylinders  produced  by  the  shrinkage,  the 
system  being  at  rest.      The  curves  r  show  the   stresses  in  the 
cylinders   for  the    system  in  action.      The   curve   p    shows   the 
stresses  that  would  result  from  the  pressure  P0  in  a  single  cylinder. 


228 


ORDNANCE  AND  GUNNERY. 


In  each  cylinder  the  ordinates  of  the  curve  r  are  the  algebraic 

sums  of  the  ordinates  of  the  curves  p  and  s. 

The  gain  and  loss  of  strength  in  the  compound  cylinder  as 

compared  with  the  single  cylinder  are  shown  in  Fig.  49.      The 

curve  t  is  the  curve  of  tangential  stress  due  to   the  maximum 

permissible  interior  pressure  in 
the  single  cylinder.  The  gain 
in  strength  in  each  cylinder  of 
the  compound  cylinder  is  shown 
by  the  cross-shaded  area  marked 


FIG.  48. 


FIG.  49. 


with  the  plus  sign,  and  the  loss  in  strength  by  the  single- 
shaded  area  marked  with  the  minus  sign.  The  total  tangential 
stress  in  the  single  cylinder  is  the  area  between  the  curve  t 
and  the  horizontal  axis.  The  inner  cylinder  of  the  compound 
cylinder  gains  over  an  equal  portion  of  the  single  cylinder  the 
shaded  area  below  the  axis,  representing  the  compressive  stress 
due  to  the  shrinkage;  and  loses  the  area  between  the  curves  t 
and  r,  since  the  single  cylinder  would  be  under  the  stress  t  while 
the  compound  cylinder  is  subjected  only  to  the  lower  stress  r- 
The  outer  cylinder  at  rest  being  under  the  stress  of  extension 
represented  by  the  area  under  the  curve  s,  that  area  is  lost  to  it  in 
action,  as  compared  with  the  single  cylinder,  while  it  gains  the 
area  lying  between  the  curves  r  and  t. 

136.  Problems. — 5.  A  section  of  the  2.38  inch  experimental 
field  rifle,  model  of  1905,  has  the  following  dimensions:  R0  =  1.19 


GUNS.  229 

inches,  #i  =  1.95,  R2  =  3.  What  is  the  elastic  resistance  of  this 
section  assembled  to  offer  the  maximum  resistance,  and  what 
is  the  absolute  shrinkage?  The  elastic  limit  of  the  metal,  nickel 
steel,  is  65,000  Ibs.  per  sq.  in. 

Pie  =  23243  Ibs.  PQg  =  55184  Ibs. 

P0p  =  51875  Ibs. 
Pl8  =  9158  Ibs.  Si=  0.00554  in. 

6.  The  prescribed  shrinkage  for  the  above  section  is  0.005  of 
an  inch.  What  is  the  elastic  resistance  of  the  section  with  this 
shrinkage  and  what  is  the  stress  of  tangential  compression  on 
the  bore? 

Pl8  =  8271  Ibs.  Pott  =  53527  Ibs. 

It  =  0.000879  in.  St  =  26360  Ibs. 

137.  Systems  Composed  of    Three  and  Four  Cylinders. — 

The  construction  and  elastic  strength  of  the  larger  guns  built 
up  of  three  or  four  cylinders  are  determined  by  considerations 
similar  to  those  explained  in  the  foregoing  discussion.  Precau- 
tion is  taken,  by  modifying  the  shrinkages  if  necessary,  that  the 
inner  cylinders  at  rest  shall  not  be  injured  by  the  shrinkage  pressures 
of  the  outer  cylinders.  The  elastic  strength  of  the  system,  that 
is,  the  maximum  permissible  interior  pressure,  is  the  pressure  that 
will  bring  any  one  of  the  elementary  cylinders  to  its  elastic  limit 
of  extension  or  compression.  In  a  proper  construction  the  tube 
is  subjected  to  the  greatest  pressures  both  at  rest  and  in  action, 
and  consequently  if  the  elastic  strength  of  the  gun  is  exceeded 
by  the  powder  pressure  the  tube  will  yield  first. 

In  Fig.  50  are  shown  the  curves  of  stress  in  a  section  through 
the  powder  chamber  of  the  8  inch  gun,  model  of  1888. 

The  curves  Si  show  the  stresses  due  to  the  assembling  of  the 
jacket  on  the  tube,  the  curves  s2  the  stresses  due  to  the  shrinkage 
of  the  outer  hoop.  The  curves  sr  show  the  resultant  stresses 
due  to  both  shrinkages. 

The  numbers  on  all  curves  are  the  actual  values  of  the 
stresses  in  tons  per  square  inch  due  to  an  interior  pressure 
Po  =  23.2  tons. 


230 


ORDNANCE  AND  GUNNERY. 


The  curve  p  shows  the  stresses  that  would  be  produced 
by  this  pressure  in  a  single  cylinder  of  the  same  dimensions 

as  the  compound  cylinder. 

The  curves  r,  the  stresses  in  ac- 
tion, are  the  resultants  of  the  curves 
sr  and  p  in  each  cylinder. 

The  curve  t  shows  the  stresses 
resulting  in  a  single  cylinder  from  the 
maximum  interior  pressure,  12.4  tons, 
permissible  in  a  single  cylinder  of 
these  dimensions. 

The  area  between  the  curves  p 
and  t  represents  the  gain  in  strength 
due  to  the  compound  construction. 
Minimum  Number  of  Cylinders 
for  Maximum  Resistance. — It  will 
be  noticed  in  Fig.  50  that  although  in 
action  all  the  cylinders  are  stretched 
to  their  elastic  limits  the  compression 
of  the  tube  at  rest  is  less  than  the 
elastic  limit  of  compression  p,  assumed 
equal  to  6.  In  this  construction 
therefore  there  was  not  obtained  the 
maximum  resistance  that  the  metal  was  capable  of  offering.  The 
same  conditions  exist  in  the  two  cylinder  gun,  as  may  be  seen  in 
Problem  2.  The  stress  of  tangential  compression  at  the  surface 
of  the  bore  at  rest  is  found  in  that  problem  to  be  22,839  Ibs.,  while 
the  elastic  limit  of  the  metal  is  50,000  Ibs. 

It  may  be  shown  by  the  equations  that  in  a  two  or  three  cylinder 
gun  whose  parts  have  essentially  the  same  elastic  limits  the  con- 
ditions that  the  parts  shall  be  strained  to  the  elastic  limit  in 
action  and  that  the  tube  shall  be  compressed  to  its  elastic  limit 
at  rest  are  incompatible.  That  both  these  conditions  may  be 
fulfilled  the  compound  cylinder  must  be  composed  of  at  least 
four  parts. 

138.  Graphic  Construction.  Three  Cylinders. — The  equations 
deduced  for  the  compound  cylinder  of  two  parts  are  used  for  the 
cylinder  of  three  parts,  the  subscripts  and  radius  ratios  in  these 


FIG.  50. 


GUNS.  231 

equations  being  changed  as  required.  Due  to  the  application  of 
the  third  cylinder  the  relation  between  the  variations  in  pressure 
in  the  bore  and  at  the  first  contact  surface,  equation  (43),  takes 
the  form 


and  between  the  first  and  second  contact  surfaces,  see  equation  (34), 

a(c—  b) 


The  shrinkage  at  the  second  surface  of  contact,  equation  (54), 
becomes 

4fl2b(c-l) 
S2~E(b-l)(c-b)P2* 

In  addition  we  need  for  the  graphic  representation  the  pressure 
at  the  first  contact  surface  due  to  the  shrinkage  pressure  at  the 
second  surface.  This  is  given  by  the  equation 


in  which  pi2  represents  that  part  of  the  pressure  at  the  first  contact 
surface  that  is  due  to  P28  only. 

Equation  (60)  also  gives  the  value  of  the  variation  in  the  pres- 
sure at  the  first  contact  surface  due  to  a  variation  in  P2g.  The 
equation  is  deduced  by  equating  the  stresses  at  R0  clue  to  the 
pressures  p\2  and  P2s. 

With  the  above  equations  we  may  now  proceed  to  the  graphic 
representation  of  the  pressures  and  shrinkages  shown  in  Fig.  51. 
We  will  call  the  three  cylinders  in  order  from  the  center  outwards 
the  tube,  the  jacket,  and  the  hoop. 

The  first  quadrant  of  the  figure,  similar  to  Fig.  45,  refers 
to  the  tube  and  the  shrinkage  at  the  first  contact  surface.  The 
second  quadrant  shows  the  pressures  on  the  surface  of  the  jacket. 
The  shrinkage  at  the  second  contact  surface  is  put  in  the 
third  quadrant  for  convenience.  The  numbers  of  the  equations 


232 


ORDNANCE  AND  GUNNERY. 


GUNS.  233 

from  which  the  lines  are  derived  are  shown  on  the  lines.  It  will 
be  understood  that  the  subscripts  and  radius  ratios  in  any  equa- 
tion must  be  such  as  make  the  equation  refer  to  the  particular 
cylinder  to  which  it  is  applied. 

P26  is  first  determined  from  equation  (37).  It  will  stretch 
the  inner  surface  of  the  hoop  to  its  elastic  limit  in  action.  It  is 
therefore  the  greatest  pressure  that  may  be  permitted  on  the 
exterior  of  the  jacket.  Draw  ab,  to  P2Pu,  and  be.  c  is  the  pres- 
sure PI  that,  acting  on  the  interior  of  the  jacket,  will  produce  the 
limiting  pressure  P2e  on  the  exterior.  Draw  cd,  to  PiP00,  and 
de.  e  is  the  value  of  P0  in  action  that  will  produce  the  value 
c  of  PI  and  therefore  the  limiting  pressure  P2S  on  the  interior  of 
the  hoop. 

When  the  system  passes  from  action  to  rest  the  pressure  on 
the  outer  surface  of  the  tube  falls  along  the  line  df  drawn  parallel 
to  piPo.  f  is  the  total  pressure  on  the  exterior  of  the  tube  at 
rest.  It  is  composed  of  the  pressure  Pi8  due  to  the  first  shrinkage 
and  the  pressure  pi2  due  to  the  second  shrinkage. 

The  pressure  on  the  outer  surface  of  the  jacket  falls  along  the 
line  bg  parallel  to  p2pi,  which  line  shows  the  relation  existing 
between  the  variations  in  pressure  at  the  two  surfaces  of  the 
jacket.  As  the  change  in  interior  pressure  on  the  jacket  stops 
at  /  the  change  in  the  exterior  pressure  stops  at  g,  and  projecting 
g  to  h  on  the  axis  of  P2  we  find  the  pressure  P2s  on  the  exterior 
of  the  jacket  at  rest.  This  is  the  shrinkage  pressure,  and  drawing 
hi  and  ij  we  find  the  shrinkage  \  that  will  produce  the  pressure 

P28. 

The  total  pressure  /  on  the  exterior  of  the  tube  is  composed 
of  the  pressure  due  to  the  first  shrinkage  and  the  pressure  due 
to  the  second  shrinkage.  The  variation  in  interior  pressure  on 
the  jacket  due  to  variation  in  the  exterior  pressure  is  given  by 
equation  (60),  which  is  represented  in  the  figure  by  the  line  p\2P28. 
If  therefore  we  draw  gk  parallel  to  this  line  the  point  k  will  be  the 
interior  pressure  on  the  jacket  when  the  exterior  pressure  is  0, 
that  is  before  the  second  shrinkage.  The  pressure  k  is  therefore 
the  pressure  due  to  the  first  shrinkage  only,  and  the  shrinkage 
that  will  produce  it  is  obtained  by  drawing  the  lines  kl  and  Im. 

For  the  system  to  be  safe  the  total  pressure  /  on  the  exterior 


234  ORDNANCE  AND  GUNNERY. 

of  the  tube  must  be  less  than  the  maximum  permissible  pressure 
as  given  by  the  last  half  of  equation  (47) .  We  will  now  designate 
the  maximum  permissible  pressure  on  the  exterior  of  the  tube 
by  Pi«(max)>  since  PIP  designates  now  an  interior  pressure  on  the 
jacket. 

The  values  of  the  pressures  and  shrinkages  marked  on  the 
figure  apply  to  the  chamber  section  of  the  6-inch  rifle,  model 
1905,  the  section  being  assembled  to  offer  the  maximum  resistance. 
For  the  section, 

Ro  =  4     inches  00  =  46000  Ibs.  per  sq.  in. 

#!=5.9  01=48000 

R2  =  8.35  62  =  47700  assumed,  53000  actual 

#3  =  12  6  =  P 

The  equations  become  with  this  data, 

(37)  P20  =  14857  (38)  P0<,  =  15159  +  1. 2 197Pi 

(38)  Pi,  =  14425  +  1.2003P2  (39)  P0,  =  24205  +0.64920Pi 

(39)  plp  =  24023 +0.6664P2  (57)       pi=0.39209P0 
(43)  p2  =  0.33963pv  (54)  Pla  =  446400Si 
(60)  p12  =  0.70129P28  (47)  Pls(max)  =  12428 
(59)  P28  =  401610S2 

139.  Wire  Wound  Guns. — As  shown  in  Fig.  50  the  various 
cylinders  of  a  built  up  gun  are  strained  to  the  elastic  limit  at  the 
interior  surfaces  only.  It  is  apparent  that  if  the  same  thickness 
of  wall  is  composed  of  a  greater  number  of  cylinders,  each  cylinder 
being  brought  to  its  elastic  limit  at  the  interior  surface,  more  of  the 
total  strength  of  the  metal  will  be  utilized.  It  follows  that 
with  a  greater  number  of  cylinders  the  gun  may  be  given  the  same 
elastic  strength  with  less  thickness  of  wall. 

The  most  convenient  method  of  increasing  the  number  of  cylin- 
ders is  by  winding  wire  under  tension  around  the  tube  of  the  gun. 
The  tension  of  the  successive  layers  of  wire  may  be  so  regulated 
that  each  layer  will  be  strained  to  its  elastic  limit  when  the  system 
is  in  action.  Usually,  however,  the  wire  is  wound  with  uniform 


GUXS.  235 

tension.  In  the  form  of  wire  the  metal  in  the  gun  is  much  more 
likely  to  be  free  of  defects,  and  can  be  given  a  much  higher  elastic 
limit  than  when  in  the  form  of  forged  hoops.  An  elastic  limit  of 
over  100,000  pounds  is  obtained  in  steel  gun  wire. 

But  the  elastic  strength  of  the  gun  is  determined  by  the  elastic 
strength  of  the  tube  that  forms  the  bore  of  the  gun;  and  if  the 
tube  is  worked  only  within  its  elastic  limit  the  wire  wound  gun 
cannot  be  stronger  than  the  built  up  gun.  In  the  Brown  wire 
wound  gun  shown  in  Fig.  5  on  page  238,  the  wire  is  wound  with 
a  tension  of  112,000  Ibs.  per  sq.  in.,  compressing  the  inner  surface 
of  the  tube  beyond  its  elastic  limit  without  apparent  injury.  This 
gun  is  composed  of  a  lining  tube  about  which  are  wrapped  over- 
lapping sheets  of  steel  1/7  of  an  inch  thick  and  of  the  shape 
shown  in  Fig.  6  on  page  238.  The  steel  sheets  form,  about  the 
lining  tube,  an  outer  tube  which  is  afterwards  wrapped  with  wire 
from  breech  to  muzzle.  The  wire  wrapped  overlapping  sheets 
give  longitudinal  stiffness  to  the  gun.  Over  the  wire  is  shrunk 
a  steel  jacket  with  just  sufficient  tension  to  prevent  its  rotation 
upon  the  tube.  The  jacket  is  not  depended  upon  to  add  to  the 
tangential  strength  of  the  gun.  It  takes,  however,  a  part  of  the 
longitudinal  stress. 

The  Ordnance  Department  6  inch  wire  wound  gun  is  shown 
in  Fig.  4,  page  238.  The  wire,  1/10  of  an  inch  square,  is  wound 
with  a  uniform  tension  of  47,400  Ibs.  per  sq.  in.,  much  less  than  in 
the  Brown  gun.  The  wire  winding  extends  over  the  breech  and 
half  way  along  the  chase  of  the  gun. 

After  31  rounds  had  been  fired  from  each  of  these  guns  with 
velocities  of  about  3280  feet  and  pressures  of  about  45,000  pounds, 
it  was  reported  that  the  most  notable  result  observed  in  the  test  of 
the  guns  was  the  considerable  wear  of  the  rifled  bore  near  the 
seat  of  the  projectile  and  near  the  muzzle  of  the  gun.  The  wear 
of  the  bore  was  much  greater  than  in  built  up  guns  of  the  same 
caliber  fired  with  velocities  of  2600  and  3000  feet. 

This  indicates  that  the  life  of  the  wire  wound  gun  will  be  very 
short  if  fired  with  the  higher  velocities  and  pressures.  In  other 
words  we  are  unable  at  present  to  take  economical  advantage  of 
the  greater  strength  of  these  weapons.  The  wire  wound  gun  has, 
however,  a  greater  reserve  of  strength  when  fired  under  ordinary 


236  ORDNANCE  AND  GUNNERY. 

pressures  than  has  the  gun  of  the  same  dimensions  built  up  wholly 
of  steel  forgings. 

No  wire  wound  guns  have  yet  been  put  in  service  in  the  United 
States.  They  have  been  extensively  used  for  some  years  by  the 
British  Government. 


CONSTRUCTION  OF  GUNS. 

140.  General  Characteristics. — The  smaller  guns  in  our  service, 
such  as  the  mountain  gun,  the  field  and  siege  howitzers  and 
mortars,  are  made  from  single  forgings.  All  other  guns  are  built 
up.  The  smaller  built  up  guns  of  caliber  up  to  5  inches  consist  of 
a  central  tube  (see  opposite  page),  a  jacket  surrounding  the  breech 
end  of  the  tube,  and  a  locking  ring  which  locks  the  tube  and 
jacket  together.  Guns  of  caliber  greater  than  5  inches  have  one 
or  more  layers  of  hoops  surrounding  the  tube  and  jacket.  The 
bore  of  the  tube  forms  the  powder  chamber,  the  seat  of  the  pro- 
jectile, and  the  rifled  bore.  The  jacket  embraces  the  tube  from 
the  breech  end  forward  nearly  half  the  length  of  the  tube  and 
extends  to  the  rear  of  the  tube  a  sufficient  distance  to  allow  the 
seat  of  the  breech  block  to  be  formed  in  the  bore  of  the  jacket. 
Through  the  bearing  of  the  breech  block  in  the  jacket  the  longi- 
tudinal stress  due  to  the  pressure  of  the  powder  gases  is  trans- 
mitted to  the  jacket  and  the  metal  of  the  tube  is  thus  relieved 
from  this  stress. 

All  guns  of  6  inch  caliber  and  above  are  hooped  to  the  muzzle. 
The  6  and  8  inch  guns  have  a  single  layer  of  hoops  over  the  jacket. 
Guns  of  caliber  larger  than  8  inches  have  two  layers  of  hoops 
over  the  jacket. 

The  construction  of  the  several  classes  of  guns  and  mortars 
of  the  latest  models  may  be  seen  in  the  illustrations,  pages  237 
and  238. 

The  forward  end  of  the  jacket  of  the  field  and  siege  rifles  is 
threaded  with  a  broad  screw  thread.  The  rear  end  of  locking 
hoop  is  provided  with  a  similar  female  thread,  and  the  locking 
hoop  is  both  screwed  and  shrunk  on  the  jacket.  The  hoop  is  also 
shrunk  to  the  tube,  and  by  means  of  a  bearing  against  a  shoulder 


GUNS. 


237 


on  the  tube  just  forward  of  the  jacket  it  holds  the  tube  and  jacket 
firmly  together. 


A  noteworthy  difference  will  be  observed  in  the  construction 
of  the  two  12  inch  rifles,  Figs.  1  and  2,  page  238.    While  the  gun 


r 


n 

J 


t      I 
01     »» 

Shi 


ZD; 


I 

(= 


j 


GUNS.  239 

of  the  older  model,  34  calibers  long,  is  composed  of  a  tube  and 
jacket  and  17  hoops,  the  gun  of  later  model,  40  calibers  long,  is 
composed  of  tube  and  jacket  and  but  7  hoops.  The  reduction  in 
the  number  of  the  hoops  by  increasing  their  lengths  has  been 
made  possible  by  the  great  advances  that  have  been  made  in 
recent  years  in  the  production  of  large  masses  of  steel  of  the 
requisite  high  quality.  The  improvement  has  been  largely  due 
to  the  demand  of  the  Ordnance  Department,  and  to  the  stringent 
and  increased  requirements  in  successive  specifications  for  gun 
forgings. 

By  the  increase  in  the  size  of  the  hoops  there  has  been  gained, 
in  addition  to  ease  and  economy  of  manufacture,  largely  in- 
creased longitudinal  strength  and  stiffness  in  the  gun,  which 
permits  the  construction  of  a  longer  gun  without  the  tendency  to 
droop  at  the  muzzle. 

The  D  hoop  shown  in  Fig.  2,  page  238,  locks  together  the  jacket 
and  the  C\  hoop;  and  these,  bearing  against  shoulders  on  the 
tube,  in  rear  and  in  front,  hold  the  tube  firmly  in  place.  The 
space  behind  the  D  hoop,  left  to  accommodate  the  increase  of 
length  of  the  hoop  when  heated  for  shrinking,  is  filled  with  a  steel 
filling  ring  as  noted  in  the  1888  model.  The  joint  between  the 
Ci  and  C-2  hoops  is  coned,  as  shown  exaggerated  in  Fig.  52.  Four 
securing  pins  passing  through  the  €2  hoop  near  the  muzzle  assist 
in  preventing  forward  movement  of  the  — 
hoops  under  the  vibration  set  up  in  the 
gun  by  the  shock  of  discharge. ^— 

As  the  metal  at  the  muzzle  receives 

support  from  one  side  only  the  gun  is  thickened  there  to  make 
the  section  of  equal  strength  with  those  near  it.  The  thickening 
of  the  metal  produces  what  is  called  the  swell  of  the  muzzle. 

141.  Operations  in  Manufacture. — The  steel  forgings  from 
which  the  parts  of  the  guns  are  made  are  manufactured  by  private 
concerns  and  are  delivered  rough  bored  and  turned  to  within 
about  3/10  of  an  inch  of  finished  dimensions. 

As  the  parts  of  the  gun  are  of  a  general  cylindrical  form  the 
principal  operations  in  preparing  them  for  assembling  are  the 
operations  of  boring  and  turning. 

In  making  long  bores  of  comparatively  small  diameter,  as  in 


240  ORDNANCE  AND  GUNNERY. 

the  tubes  of  guns,  special  tools  are  necessary  in  order  to  insure 
straightness  of  the  bore. 

The  tube  is  carefully  mounted  in  the  lathe  and  so  centered  that 
any  bending  or  warping  that  may  exist  in  the  long  forging  will  be 
wholly  removed  in  the  operations  of  boring  and  turning.  The 
bore  is  started  true  with  a  small  lathe  tool  and  continued  for  a 
length  of  about  three  calibers.  The  tool  shown  in  Fig.  53  is  then 


FIG.  53. 

used  to  continue  the  bore.  This  tool,  called  a  reamer,  has  a  semi- 
cylindrical  cast  iron  body,  or  bit,  A,  carrying  the  steel  cutting 
tool  B.  It  is  supported  in  the  boring  bar  C,  which  is  pushed 
forward  by  the  feed  screw  of  the  lathe.  The  semi-cylindrical  bit 
exactly  fits  in  the  bore  already  started.  As  the  tube  rotates,  the 
pressure  against  the  cutting  edge  B  forces  the  bit  against  the 
bottom  of  the  bore.  This  together  with  the  length  of  the  bit 
prevents  deviation  of  the  cutting  edge  as  the  tool  advances  down 
the  bore,  and  makes  the  bore  a  true  cylinder. 

In  order  to  make  the  surface  of  the  bore  smooth  and  uniform 
the  light  finishing  cuts  are  made  with  a  packed  bit  or  wood  reamer, 
shown  in  Fig.  54. 


D 


C 


D 


FIG.  54. 

The  cast  iron  bit  A  carries  two  cutters,  6,  at  opposite  ex- 
tremities of  a  diameter.  Two  pieces  D  of  hard  wood  packing  are 
bolted  to  the  bit  and  serve  to  guide  the  cutters  accurately.  The 
tool  fits  tightly  in  the  bore.  The  light  cut  taken  and  the  pressure 
of  the  oiled  wood  packing  leaves  the  surfaces  of  the  bore  very 
smooth  and  uniform  and  highly  polished. 

142.  Gun  Lathe. — The  general  features  of  the  lathe,  by  means 
of  which  thev  larger  forgings  are  bored  and  turned,  are  shown  in 


GUNS. 


241 


Fig.  55.  The  principal  parts  are:  the  bed,  B,  made  very  strong 
and  much  larger  than  for  the  ordinary  lathe;  the  head  stock  and 
cone  pulley  C;  the  face  plate  F,  to  which  the  work  T  is  clamped; 
the  slide  rest  S,  carrying  a  cutting  tool;  the  back  rests  R,  forming 
intermediate  supports  for  the  tube  T;  the  boring  bed  0,  supported 
on  the  bed  proper,  B,  and  carrying  the  boring  bar  P  with  its 
tool  Q;  the  feed  screw  V,  which  lies  inside  the  boring  bar  P;  and 
the  gears  W,  by  which  the  feed  screw  is  driven. 

Motion  is  communicated  to  all  the  parts  by  the  belt  X,  acting 
on  the  cone  pulley.  This  causes  the  face  plate  and  tube  to  rotate 
and  also  communicates  motion  to  the  long  shaft,  not  shown  in 
the  figure,  upon  the  end  of  which  is  the  lower  gear  wheel  W". 
The  motion  is  transmitted  through  W  to  W,  and  thence  to 


FIG.  55. 


the  feed  screw  V.  By  changing  the  gears  any  ratio  between  the 
velocity  of  rotation  of  the  tube  and  that  of  translation  of  the  tool 
Q  can  be  obtained.  It  is  necessary  that  there  be  only  one  source 
of  motion,  since  if  the  feed  screw  or  slide  rest  were  driven  inde- 
pendently of  the  cone  pulley  which  drives  the  work,  a  change  in 
the  speed  of  one  would  not  cause  a  corresponding  change  in  the 
speed  of  the  others,  and  damage  to  the  tools,  the  work,  or  the 
machine  might  result. 

The  slide  rest  S  is  driven  by  a  second  feed  screw  not  shown. 

The  back  rests  R  can  be  adjusted  to  any  diameter  of  forging. 

The  lathe  is  supplied  with  an  oil  pump,  by  means  of  which  a 
stream  of  oil  is  forced  into  the  bore  while  the  work  is  in  progress. 
The  chips  or  cuttings  come  out  at  the  opposite  end  of  the  tube 
from  that  at  which  the  tool  enters. 

Boring  and  Turning  Mill. — The  smaller  hoops  are  usually 
machined  on  a  vertical  boring  and  turning  mill,  shown  in  Fig.  56. 
The  work  is  bolted  to  the  slotted  table  t.  The  cutting  tools 
are  carried  in  the  tool  holders  o  at  the  lower  ends  of  the  boring 


242  ORDNANCE   AND  GUNNERY. 

bars  a.  In  the  illustration  one  of  the  boring  bars  is  shown  in  a 
vertical  position  and  the  other  inclined.  The  table  rotates, 
carrying  the  work  with  it.  By  means  of  the  feed  mechanism 
the  cutting  tools  are  fed  either  vertically  or  horizontally  or  at  an 
angle  as  desired. 

On  account  of  the  greater  difficulty  of  boring  than  of  turning 
to  prescribed  dimensions,  the  bored  shrinkage  surface  is  always 
finished  first.  Allowance  may  then  be  made  in  turning  the  male 
surface  for  any  slight  error  in  the  diameter  of  the  bored  surface. 
The  desired  shrinkage  is  thus  obtained. 

143.  Assembling. — The  interior  diameter  of  the  jacket,  when 
bored  to  finished  dimensions,  is  less  than  the  exterior  diameter 
of  the  tube  by  the  amount  of  the  shrinkage  prescribed.  In  order 
to  assemble  the  jacket  on  the  tube  it  is  therefore  necessary  to 
expand  the  jacket  sufficiently  to  permit  its  being  slipped  over 
the  tube  into  its  place.  The  expansion  is  accomplished  by  heat. 
The  jacket  is  placed  in  a  vertical  furnace  heated  by  oil  or  other 
fuel  to  a  temperature  varying  from  600  to  750  degrees  Fahrenheit, 
depending  upon  the  thickness  of  the  forging  and  the  amount  of 
expansion  required.  Great  care  is  exercised  that  the  heating 
shall  be  uniform  throughout  the  length  of  the  forging.  The 
requisite  expansion,  which  in  general  is  about  0.004  of  an  inch 
per  inch  of  diameter,  is  determined  by  a  gauge  set  to  the  exact 
diameter  to  which  the  bore  should  expand.  The  gauge,  held  at  the 
end  of  a  long  rod,  is  tried  in  the  bore  of  the  forging  in  the  furnace. 
When  it  enters  the  bore  properly  the  requisite  expansion  has 
been  attained.  Care  is  taken  to  avoid  overheating  which  might 
injuriously  affect  the  qualities  of  the  metal. 

When  the  desired  expansion  has  been  attained  the  jacket  is 
hoisted  vertically  from  the  furnace.  It  will  be  seen  by  reference 
to  the  figures  on  page  238  that  the  shoulders  on  the  tubes  of  the 
12-inch  guns  are  so  arranged  that  the  jacket  must  be  slipped  over 
the  breech  end  of  the  tube,  while  the  arrangement  of  the  shoulders 
on  the  wire  wrapped  tubes  of  the  6-inch  guns  require  that  the 
tube  be  inserted  into  the  breech  end  of  the  jacket. 

The  method  of  assembling  is  called  breech  insertion  or  muzzle 
insertion  according  as  the  breech  or  muzzle  end  of  the  jacket  first 
encircles  the  tube.  For  breech  insertion,  as  in  wire  wrapped 


FIG.  56. — Vertical  Boring  and  Turning  Mill,  37-inch. 


GUNS. 


243 


guns,  the  jacket  after  being  lifted  from  the  surface  is  placed  up- 
right on  a  strong  iron  shelf  supported  at  the  mouth  of  a  deep  pit, 
Fig.  57.  The  tube  is  then  carefully  lowered  into  its  seat  in  the 
jacket.  For  muzzle  insertion,  as  in  the  12-inch  guns,  the  tube 
is  supported  upright  in  the  pit,  the  breech  end  up,  and  the  jacket 
is  lowered  over  the  tube. 

Cooling  of  the  heated  jacket  is  accomplished  by  means  of 
sprays  of  water  directed  against  the  forging  from  an  encircling 
pipe  as  shown  at  D  in  Fig.  58.  The  cooling  is  begun  at  the  section 
of  the  jacket  which  it  is  desired  should  take  hold  of  the  tube  first, 


D 


--TUBE. 


J 


-JACKET. 


FIG.  57. 


FIG.  58. 


as  at  the  shoulder  C,  Fig.  58.  As  the  cooling  of  the  remainder  of 
the  jacket  progresses  the  metal  is  drawn  toward  the  section  first 
cooled,  and  thus  a  tight  joint  at  the  shoulder  is  insured.  After 
the  jacket  has  gripped  at  the  shoulder  the  cooling  pipe  is  moved 
very  gradually  upward  toward  the  breech,  care  being  exercised 
that  the  jacket  shall  grip  at  successive  sections  in  order  that  longi- 
tudinal stresses  due  to  unequal  contraction  may  not  be  developed 
in  the  metal. 

The  shrinking  on  of  hoops  is  conducted  in  practically  the  same 
manner  as  the  shrinking  of  the  jacket.  When  the  hoops  are  small 
and  can  be  handled  quickly  they  are  often  assembled  to  the  gun 
in  a  horizontal  position.  Cooling  of  the  hoop  is  begun  at  the  end 


244  ORDNANCE  AND  GUNNERY. 

toward  the  jacket,  or  toward  the  hoop  already  in  place,  in  order 
that  contraction  shall  take  place  in  that  direction  and  make  a 
tight  joint  between  the  parts. 

When  the  assembling  of  all  the  parts  is  completed  the  tube  is 
finish  smooth-bored  and  the  exterior  of  the  gun  turned  to  pre- 
scribed dimensions. 

144.  Rifling  the  Bore. — The  rifling  of  the  bore  is  effected  in 
the  rifling  machine,  which  is  essentially  similar  to  the  boring 
and  turning  lathe  previously  described.  The  gun  does  not  rotate 
in  the  rifling  machine,  but  the  cutting  tool  is  given  the  combined 
movement  of  translation  and  rotation  necessary  to  cut  the  spiral 
grooves  in  the  bore.  The  rifling  bar  takes  the  place  of  the  boring 
bar,  P  Fig.  55.  The  rifling  bar,  m  Fig.  59,  carrying  at  its  forward 
-e 


£XO 


FIG.  59. 

end  the  rifling  tool  g  provided  with  cutters  for  the  grooves,  is  moved 
forward  and  backward  by  means  of  the  feed  screw  b.  The  desired 
motion  of  rotation  is  given  to  the  rifling  bar  by  means  of  the 
pinion  c  and  the  rack  d,  which  engages  on  a  guide  bar  e  bolted  to 
a  table  made  fast  to  the  side  of  the  rifling  bar  bed.  The  bar  e 
is  flexible  and  is  given  the  shape  of  the  developed  curve  of  the 
rifling.  As  the  rack  travels  forward  with  the  rifling  bar  it  is  forced 
to  the  left  by  the  guide  bar,  imparting  the  proper  amount  of 
rotation  to  the  rifling  bar  and  cutting  tools. 

Cutting  tools  are  carried  at  both  ends  of  a  diameter  of  the 
rifling  tool.  At  the  end  of  a  cut  the  cutting  tools  are  automatically 
withdrawn  toward  the  center  of  the  bar  and  the  bar  retracted  for 
a  new  cut. 

When  a  number  of  guns  of  the  same  design  are  to  be  manu- 
factured, a  spiral  groove  is  cut  in  the  rifling  bar  itself.  A  stud 
fixed  in  the  forward  support  of  the  rifling  bar  works  in  the  groove 
and  gives  to  the  bar  the  proper  movement  of  rotation.  The  guide 
bar  with  rack  and  pinion  is  not  then  used. 


GUNS. 


245 


MEASUREMENTS. 

145.  Necessity  of  Accurate  Measurements. — In  order  that  the 
gun  may  be  assembled  with  the  required  shrinkages  the  surfaces  of 
the  various  cylinders  composing  the  gun  must  be  accurately  turned 
and  bored  to  the  prescribed  dimensions.  The  dimensions  of  all 
parts  of  the  gun  must  be  in  accord  with  the  design.  The  toler- 
ances, or  allowed  variations  from  prescribed  dimensions,  are  in 
general  two  thousandths  of  an  inch  for  the  diameters  of  shrinkage 
surfaces,  and  one  hundredth  of  an  inch  in  lengths. 

Accurate  measurements  of  the  various  dimensions  of  every 
part  of  a  gun  are  therefore  essential. 

The  exact  length  of  any  dimension  of  a  forging  is  usually 
obtained  by  means  of  one  of  two  instruments,  called  measuring 
points  and  calipers.  The  points  of  the  instrument  used  are 
adjusted  until  the  distance  between  them  is  the  exact  length  of 
the  dimension  to  be  determined.  The  length  between  the  points 
of  the  instrument  is  then  measured  in  a  vernier  caliper. 

Vernier  Caliper. — The  vernier  caliper  is  shown  in  Fig.  60. 
The  steel  blade  a  graduated  in  inches  and  decimal  divisions  is  pro- 


L  ' 

!     ! 

c 

>                 a 

iiiiliiiiliiiiiHiiliiiiliiiiiiiiilmmii! 

1 

mi.'/ii 

'  |llll 

z\ 

t'\'',;  .'       '       ' 

ii 

d 

3, 

,  nnliiiilmilimlmiliiii 

[ 

( 

5     1 
|U 

in 

2) 

_»J 

23 

6 

o 

e 

/ 

L 

1 

FIG.  60. 

vided  with  a  fixed  jaw  b  and  movable  jaw  c.  By  means  of  the 
clamp  d  and  small  motion  screw  e  the  movable  jaw  may  be  brought 
accurately  to  any  distance  from  the  fixed  jaw.  The  distance 
between  the  jaws  is  read  from  the  scale  and  vernier.  The  least 
reading  of  the  vernier  is  one  thousandth  of  an  inch.  The  ends  of 
the  jaws  6  and  c  are  usually  one  eighth  of  an  inch  wide  so  that  the 
measurement  between  their  outer  edges  is  a  quarter  of  an  inch 
greater  than  the  reading  of  the  scale. 


246 


ORDNANCE  AND  GUNNERY. 


Measuring  Points.  —  The  measuring  point  consists  ordina- 
rily of  a  rod  of  wood  into  the  ends  of  which  are  set  metal  points, 
Fig.  61.  One  of  these  points  at  least  is  capable  of  a  small  move- 
ment out  and  in.  The  rod  is  of  wood  in  order  that  the  heat  of 
the  hand  may  not  affect  its  length.  One  of  the  metal  points  may 


FIG.  61. 

be  provided  with  a  micrometer  head  from  which  the  movement 
of  the  point  out  and  in  from  a  fixed  length  may  be  read  at  once. 

Measuring  points  are  used  in  determining  interior  diameters 
and  the  distance  between  surfaces  that  face  each  other.  In 
measuring  an  interior  diameter  at  any  point  in  a  bore,  as  at  a,  Fig. 
62,  one  end  of  the  measuring  point  is  placed  at  a.  As  the  diam- 
eter is  the  longest  line  in  the  cross  section,  the  end  6  'must  be 
moved  out  until  the  rod  cannot  be  revolved  about  the  end  a  in 
the  plane  of  the  cross  section. 

To  determine,  when  touch  is  made  at  6,  that  the  rod  is  truly  in 
the  cross  sectional  plane  the  rod  must  be  revolved  in  a  direction 
at  right  angles  to  this  plane,  for  as  seen  in  Fig.  63  the  diameter  is 


s 


5r 


c 


FIG.  62. 


FIG.  63. 


the  shortest  line  in  the  longitudinal  plane,  and  the  rod  when  set 
to  the  proper  length  must  be  capable  of  revolution  in  that  plane, 
touching  only  at  the  point  b.  In  other  words  the  measuring 
point  has  the  length  of  the  diameter  when  the  measuring  point 
is  incapable  of  revolution  in  the  cross  sectional  plane  and  at  the 
same  time  capable  of  revolution  in  the  longitudinal  plane. 


GUNS.  247 

Similarly  when  applying  the  rod  to  the  vernier  caliper  to  read 
the  length  of  the  rod,  the  movable  jaw  of  the  caliper  must  be 
brought  to  such  a  distance  from  the  fixed  jaw  that  the  rod  when 
revolved  about  one  end  in  two  planes  at  right  angles  to  each  other 
will  touch  at  one  point  only  in  each  plane  of  movement.  The 
length  of  the  interior  diameter  may  then  be  correctly  read  from 
the  scale  of  the  caliper. 

In  making  measurements  the  sense  of  touch  is  depended  upon 
to  determine  when  contact  exists.  When  the  distance  that 
separates  a  measuring  point  from  a  surface  is  so  minute  that  light 
cannot  be  seen  between  the  point  and  the  surface,  the  lack  of 
contact  can  be  unerringly  detected  by  the  touch. 

146.  The  Star  Gauge. — In  the  case  of  long  tubes  all  parts  of 
which  are  not  readily  accessible  some  means  must  be  adopted  of 
making  the  measurements  at  a  distance  from  the  operator.  The 
instrument  used  for  this  purpose  is  called  a  star  gauge. 

Its  general  features  are  shown  in  Fig.  64.     The  long  hollow 


a 


gyO 


"tf  FIG.  64. 

rod  or  staff  a  carries  at  its  forward  end  the  head  6.  Embracing 
the  rear  end  of  the  staff  is  the  handle  c  to  which  is  attached  the 
square  steel  rod  /.  The  handle  has  a  sliding  motion  or  screw 
motion  on  the  end  of  the  staff,  and  any  movement  of  the  handle 
is  communicated  through  the  rod  /  to  the  cone  g  in  which  the 
square  rod  terminates  at  its  forward  end. 

The  head  b  has  three  or  more  sockets,  d,  which  are  pressed  in- 
ward upon  the  cone  g  by  spiral  springs  not  shown  in  the  figure. 
Into  these  sockets  are  screwed  the  star  gauge  points  e.  Three 
points  are  generally  used,  120°  apart.  The  points  are  of  different 
lengths  for  the  different  calibers  to  be  measured. 

Any  movement  of  the  cone  forward  or  backward  causes  a  cor- 
responding movement  of  the  measuring  points  out  or  in.  The 
cone  has  a  known  taper,  and  the  change  in  its  diameter  under  the 


248  ORDNANCE  AND  GUNNERY. 

measuring  points  due  to  any  movement  of  the  handle  is  marked 
on  a  scale  at  the  handle  end  of  the  staff.  The  handle  carries  a 
vernier  by  means  of  which  the  scale  may  be  read  to  a  thousandth 
of  an  inch.  The  reading  of  the  scale  is  the  change  in  length  of 
the  diameter  that  is  measured  by  the  points  when  the  handle  is 
at  the  zero  mark. 

The  staff  a  and  rod  /  are  made  in  sections,  usually  50  inches 
long,  so  that  the  gauge  may  be  given  a  length  convenient  for  the 
measurement  of  any  length  of  bore. 

The  star  gauge  is  set  for  any  measurement  by  means  of  a  stand- 
ard ring  of  the  proper  diameter.  The  standard  rings  are  of  steel, 
hardened  and  very  carefully  ground  to  the  given  diameter.  If  it 
is  desired  to  measure  a  10-inch  bore  for  instance,  measuring  points 
of  the  proper  length  are  inserted  in  the  sockets  d  of  the  star  gauge. 
The  10-inch  ring  is  held  surrounding  the  points,  and  the  handle  c 
of  the  star  gauge  is  pushed  in  until  the  points  touch  the  inner  sur- 
face of  the  ring.  The  handle  is  then  adjusted  until  the  reading  of 
the  scale  is  zero.  The  instrument  is  now  ready  for  use. 

The  gun  or  forging  whose  bore  is  to  be  measured  is  supported 
so  that  its  axis  is  horizontal.  The  star  gauge  is  also  carefully 
supported  in  the  axis  of  the  bore  prolonged,  and  in  the  bore  when 
necessary.  The  distance  of  the  measuring  points  from  the  face 
of  the  bore  is  read  from  a  scale  of  inches  marked  on  the  staff.  At 
each  selected  position  of  the  gauge  the  handle  is  pushed  forward 
until  the  measuring  points  touch  the  surface  of  the  bore.  The 
difference  between  the  diameter  of  the  bore  at  this  point  and  the 
standard  diameter  for  which  the  gauge  is  set  is  then  read  from 
the  scale  at  the  handle  in  thousandths  of  an  inch. 

147.  Calipers. — For  the  measurement  of  outside  diameters 
calipers  are  used.  The  ordinary  calipers  for  measurement  of  short 
exterior  lengths  are  shown  in  Fig.  65.  For  the  measurement  of 
the  large  exterior  diameters  of  gun  forgings,  calipers  as  shown  in 
Fig.  66  are  employed.  One  of  the  points  a  or  6  is  movable  and 
may  be  provided  with  a  micrometer  head.  As  in  the  case  of  inte- 
rior measurements  the  caliper  must  be  revolved  in  two  planes  about 
the  end  that  is  held  at  the  point  from  which  the  diameter  is  to  be 
measured,  and  the  distance  between  the  points  of  the  caliper  must 
be  adjusted  until  touch  is  made  at  one  point  only  in  each  plane. 


GUNS. 


249 


The  distance  between  the  points  of  the  caliper,  as  determined 
by  the  length  between  the  outer  edges  of  the  jaws  of  the  vernier 
caliper,  is  then  the  true  length  of  the  exterior  diameter. 


FIG.  65. 


FIG.  66. 


The  frames  of  the  large  exterior  calipers  required  for  gun  meas- 
urements must  be  made  heavy  in  order  that  the  calipers  shall  have 
sufficient  stiffness  and  not  be  subject  to  change  of  form.  In 


FIG.  67. 

use  these  calipers  are  therefore  supported  from  above  by  a 
spring  connection  with  a  frame  that  is  secured  to  the  piece  being 
measured,  Fig.  67. 

Standard  Comparator. — In  order  to  insure  accuracy  in  all 
measurements,  all  measuring  scales  are  compared  with  a  common 
standard.  For  this  purpose  the  standard  comparator  is  provided. 


250 


ORDNANCE  AND  GUNNERY. 


A  heavy  metal  bar  very  accurately  graduated  in  inches  and  deci- 
mal divisions  rests  in  a  very  stiffly  constructed  cast  iron  bed. 
Sliding  heads  on  the  bed,  one  of  which  carries  a  reading  microscope, 
may  be  set  accurately  at  any  determined  distance  apart. 

RIFLING. 

148.  Purpose. — The  purpose  of  the  rifling  in  a  gun  is  to  give  to 
the  projectile  the  motion  of  rotation  around  its  longer  axis  neces- 
sary to  keep  the  projectile  point  on  in  flight.  The  rifling  consists 
of  a  number  of  spiral  grooves  cut  in  the  surface  of  the  bore.  The 
soft  metal  of  a  band  on  the  projectile  is  forced  into  the  grooves 
by  the  pressure  of  the  powder  gases,  whereby  a  rotary  motion  is 
communicated  to  the  projectile. 

Twist. — The  twist  of  the  rifling  at  any  point  in  the  bore  is  the 
inclination  of  the  tangent  to  the  groove,  at  that  point,  to  the  axis 


of  the  bore.  Twist  is  usually  expressed  in  terms  of  the  caliber, 
as  one  turn  in  so  many  calibers.  If  the  inclination  of  the  groove 
is  constant  the  rifling  is  of  uniform  twist.  If  the  inclination  of 
the  groove  increases  from  breech  to  muzzle  the  rifling  has  an 
increasing  twist. 

Let  a,  Fig.  68,  be  the  development  of  one  turn  of  a  groove  with 
uniform  twist,  n  the  twist  in  calibers,  or  the  number  of  calibers  in 
which  the  groove  makes  a  complete  turn,  and  r  the  radius  of  the 
bore.  Then  AB  =  2nr,  BC  =  2xr,  and  we  have 


tan  <   = 


(61) 


for  the  value  of  the  tangent  of  the  angle  of  the  rifling.  For  the 
groove  with  increasing  twist  (j>  is  variable,  but  at  any  point  its 
tangent  is  ~/n. 


GUNS.  251 

Let  v  denote  the  velocity  of  the  projectile  at  any  point  of  the 

bore,  in  feet  per  second, 
<f>  the  angle  made  by  the  tangent  to  one  of  the  grooves 

with  an  element  of  the  bore, 
a>  the  angular  velocity  of  the  projectile, 
r  the  radius  of  the  bore,  in  feet. 

The  velocity  of  the  projectile  along  the  groove  is  the  resultant 
of  two  components,  v  and  v  tan  <£,  at  right  angles  to  each  other. 

The  actual  velocity  of  rotation  of  a  point  on  the  surface  of  the 
projectile  is  a>r=  cod/2,  and  this  is  equal  to  the  component  v  tan  <£. 
Therefore 

=  i?  tan  <jS     and     w  =  2r  tan  <}>/d  (62) 


Increasing  Twist.  —  When  the  twist  is  uniform  the  inclination 
of  the  grooves  to  the  axis  of  the  bore  is,  the  same  throughout 

^Jv  ,|_  »  *-*J^^joju»J*-''1^A*' 

the  length  of  the  bore,  and  therefore  ~4i-is  greater  at  the  breech 
than  the  inclination  of  the  grooves  of  an  increasing  twist  that  is 
equal  to  the  uniform  twist  at  the  muzzle.  The  pressure  required 
to  cause  the  projectile  to  take  the  grooves  is  therefore  greater  in 
the  case  of  the  uniform  twist,  and  the  greater  resistance  offered  to 
the  starting  of  the  projectile  serves  to  increase  the  maximum  pres- 
sure in  the  gun.  The  total  energy  absorbed  by  the  projectile  in 
taking  the  rifling  is  greater  with  an  increasing  twist  than  with  the 
uniform  twist  on  account  of  'the  increased  frictional  resistance  due 
to  the  continual  change  in  the  inclination  of  the  grooves.  The 
total  energy  absorbed  is,  however,  small  compared  with  that 
required  to  give  the  projectile  its  velocity  of  translation. 

149.  Equation  of  the  Developed  Curve  of  the  Rifling.  —  If 
the  twist  increases  from  zero  at  the  breech  uniformly  to  the  muzzle, 
the  equation  of  the  developed  curve  of  the  rifling  will  be  of  the 
form 

y  =  ax  +  bx2 

which  being  differentiated  twice  gives 

d?y/dx2  =  2b 

That  is,  the  rate  of  change  in  the  tangent  to  the  groove  is  constant. 

A  twist  of  this  form  would  offer  less  resistance  than  the  uni- 

form twist  to  the  initial  rotation  of  the  projectile.     But  to  still 


252  ORDNANCE  AND  GUNNERY. 

further  diminish  this  resistance,  a  twist  that  is  at  first  less  rapid 
than  the  uniformly  increasing  twist  and  later  more  rapid  has 
been  generally  adopted  for  rifled  guns.  The  equation  of  the 

semicubic  parabola 

(63) 


is  generally  adopted  for  the  developed  curve  of  the  rifling.  The 
twist  is  assumed  at  breech  and  muzzle  and  the  curve  between 
these  points  is  obtained  from  the  above  equation. 

The  tangent  to  the  curve  at  any  point  makes  with  the  axis  of  x 
an  angle  whose  tangent  is  dy/dx.  The  value  of  the  tangent  of 
the  angle  at  any  point  is  ?r/n,  see  equation  (61),  n  representing 
the  twist  in  calibers,  the  number  of  calibers  in  which  the  groove 
makes  a  complete  turn. 

Therefore,  differentiating  equation  (63), 


dy/dx  =  tan  $  =  3x*/4p  =  x/n  (64) 

Problem  i.  —  Determine  the  equation  of  the  developed  rifling 
curve,  and  the  part  of  the  curve  to  be  used,  for  the  3  inch  rifle, 
model  1905.  The  twist  is  0  at  the  breech  end,  1  turn  in  25 
calibers  at  a  point  12.52  inches  from  the  muzzle,  and  from  this 
point  uniform  to  the  muzzle.  The  length  of  the  rifled  bore  is 
72.72  inches. 

The  twist  at  the  breech  is  0,  or  one  turn  in  an  infinite  number 
of  calibers.  Therefore  n  in  equation  (64)  is  infinite,  tan  0  is  0 
and  x  =  0;  and  from  equation  (63)  y  is  also  0.  The  origin  of  the 
curve  is  therefore  at  the  breech. 

At  12.52  inches  from  the  muzzle,  x  =  72.72  -12.52  =  60.2,  and 
the  twist  n  =  25. 

Substituting  these  values  in  equation  (64)  and  solving  for  p, 

p  =  3(60.2)*25/47r  =  46.31 

Substituting  in  (63)  we  have  for  the  equation  of  the  developed 
groove  of  the  rifling  from  the  breech  to  a  point  12.52  inches  from 
the  muzzle 


and  the  part  of  the  curve  to  be  used  lies  between  the  origin  and 
the  ordinate  for  which  the  abscissa  is  x  =  60.2.     From  this  point 


GUNS. 


253 


to  the  muzzle  the  curve  is  a  straight  line  making  with  the  axis 
of  x  an  angle  whose  tangent  is  77/25. 

The  curve  is  shown  numbered  1  in  Fig.  69. 

150.  Problem  2. — Determine  the  equation  of  the  developed 
rifling  curve,  and  the  part  of  the  curve  to  be  used,  for  the  4.7 
inch  Armstrong  gun,  50  calibers  long.  The  twist  is  1  turn  in 
600  calibers  at  the  breech,  and  1  turn  in  30  calibers  at  the  muzzle. 
The  length  of  the  rifled  bore  is  203.12  inches. 

At  the  breech  n  =  600    and     tan  <j>  =  77/600 

At  the  muzzle  tan  (f>  =  Tr/30 

The  curve  represented  by  equation  (64)  passes  through  the 
origin  of  coordinates. 


o 


60.2  72.7a 


203.12 


FIG.  69. 


Let  x\  be  the  abscissa  of  the  point  of  the  curve  at  which  the 
tangent  is  Tr/600.  Then  x2  =  Xi+203.12  will  be  the  abscissa  of 
the  point  at  which  the  tangent  is  77/30. 

From  equation  (64) 

77/600  =  3^/47?        77/30  =  30*4  +  203.12)V4pl 
We  have  two  equations  involving  x\  and  p.     Solving  we  find 

p  =  102.2        04=0.51         x2  =  203.63 
The  equation  of  the  developed  curve  of  the  rifling  is,  equation  (63), 


And  the  abscissas  of  the  extremities  of  the  part  of  the  curve  to  be 
used  are  the  values  determined  for  x\  and  x2. 
The  curve  is  shown  numbered  2  in  Fig.  69. 


254 


ORDNANCE  AND  GUNNERY. 


Service  Rifling. — An  increasing  twist  is  adopted  for  the 
guns  in  our  service.  In  all  guns  of  recent  model  the  twist  is  one 
turn  in  50  calibers  at  the  breech,  and  increases  to  one  turn  in  25 
calibers  at  a  point  about  2£  calibers  from  the  muzzle.  The  pur- 
pose of  the  uniform  twist  for  a  short  length  at  the  muzzle  is  to 
give  steadiness  to  the  projectile  as  it  issues  from  the  bore. 

A  right  handed  twist  is  used  in  all  guns  in  our  service. 

The  number  of  grooves  depends  on  the  caliber  of  the  gun.  In 
the  siege  and  seacoast  guns  the  number  is  six  times  the  caliber  of 
the  gun  in  inches.  Thus  the  5  inch  gun  has  30  grooves  and  the 
10  inch  gun  60.  The  3  inch  field  rifle  has  24  grooves. 

The  shape  of  the  grooves  is  shown  in  Fig.  70.    The  widths  of 


FIG.  70. 

land  and  groove  noted  in  the  figure  are  the  same  for  all  guns  of 
5  inch  caliber  and  greater.  The  depth  of  the  groove  varies  from 
0.03  of  an  inch  in  the  3  inch  gun  to  0.06  in  the  seacoast  rifles,  and 
0.07  in  the  seacoast  mortars. 

A  form  of  groove  called  the  hook  section  groove,  used  in  Navy 
rifles,  is  shown  in  Fig.  71 .     The  view  is  from  the  breech  end. 


FIG.  71. 

The  driving  edge  of  the  groove  makes  a  sharp  angle  with  the 
surface  of  the  bore,  and  the  other  edge  has  a  gradual  slope  to 
that  surface. 

The  depth  of  the  groove  in  the  larger  naval  guns  is  0.05  of  an 
inch. 

In  the  service  30  caliber  rifle  the  depth  of  the  grooves  is  0.004 
of  an  inch.  It  is  desirable  in  small  arms  to  limit  the  depth  of 
the  grooves  to  the  minimum,  in  order  to  lessen  the  thickness  of 


GUNS.  255 

barrel  and  to  permit  ready  cleaning  of  the  bore.  There  are  four 
grooves  each  0.1767  inches  wide.  The  lands  are  one  third  as  wide. 
The  twist  is  uniform,  one  turn  in  10  inches. 

BREECH  MECHANISM. 

151.  General  Characteristics.— The  breech  mechanism  com- 
prises the  breech  block,  the  obturating  device,  the  firing  mechan- 
ism, and  the  mechanism  for  the  insertion  and  withdrawal  of  the 
block. 

The  breech  block  closes  the  bore  after  the  insertion  of  the  charge 
and  transmits  the  pressure  of  the  powder  gases  as  a  longitudinal 
stress  to  the  walls  of  the  gun. 

There  are  two  general  methods  of  closing  the  breech.  In  the 
first  method  the  block  is  inserted  from  the  rear.  The  block  is  pro- 
vided with  screw  threads  on  its  outer  surface  which  engage  in  cor- 
responding threads  in  the  breech  of  the  gun.  In  order  to  facilitate 
insertion  and  withdrawal  of  the  block  the  threads  on  block  and 
breech  are  interrupted. 

The  surface  of  the  block  is  divided  into  an  even  number  of 
sectors  and  the  threads  of  the  alternate  sectors  are  cut  away. 
Similarly  the  threads  in  the  breech  are  cut  away  from  those 
sectors  opposite  the  threaded  sectors  on  the  block.  The  block 
may  then  be  rapidly  inserted  nearly  to  its  seat  in  the  gun,  and 
when  turned  through  a  comparatively  small  arc,  say  1/8  or  1/12 
of  a  circle,  depending  upon  the  number  of  sectors  into  which  the 
block  is  divided,  the  threads  on  the  block  and  in  breech  are  fully 
engaged  and  the  block  locked. 

In  the  second  method  a  wedge-shaped  block  is  seated  in  a 
slot  cut  in  the  breech  of  the  gun  at  right  angles  to  the  bore,  and 
slides  in  the  slot  to  close  or  open  the  breech. 

Variations  of  these  two  methods  will  be  noted  in  the  descrip- 
tions of  the  breech  mechanism  of  some  of  the  guns  in  service. 

The  breech  block  is  usually  supported  in  the  jacket  of  the  gun 
or  in  a  base  ring  screwed  into  the  jacket.  The  seat  in  the  jacket 
being  of  greater  diameter  than  could  be  provided  in  the  tube, 
the  bearing  surface  of  the  screw  threads  on  the  block  is  increased, 
and  the  length  of  the  block  may  be  diminished. 


256 


ORDNANCE  AND  GUNNERY. 


FIG.  72. — Breech  Mechanism  for  Heavy  Guns. 


GUNS.  257 

The  Slotted  Screw  Breech  Mechanism. — The  slotted  screw 
breech  mechanism  is  better  adapted  than  any  other  for  use  in 
heavy  guns.  It  is  also  used  in  most  of  the  field  and  siege  guns 
of  our  service.  The  form  used  in  the  field  and  siege  guns  is  de- 
scribed with  the  3-inch  field  gun  in  Chapter  VIII. 

An  example  of  the  slotted  screw  breech  mechanism  as  used 
in  the  heavier  guns  is  shown  in  Figs.  72  to  74,  which  represent 
the  breech  mechanism  of  the  12-inch  rifle.  The  breech  block 
B  has  six  threaded  and  six  slotted  sectors.  When  the  breech  is 
closed  the  threads  on  block  engage  with  the  threads  in  the  breech. 
The  breech  is  opened  by  turning  the  crank  K  mounted  on  the  shaft 
W.  The  movement  of  the  crank  is  transmitted  through  the 
worm  gear  to  the  hinge  pin  HP,  and  through  the  compound  gear 
CG  to  the  rotating  lug  rl  formed  on  the  rear  of  the  block.  The 
block  is  thus  rotated  one  twelfth  of  a  turn,  and  its  threaded  sectors 
then  lie  in  the  slotted  sectors  of  the  breech.  Further  movement 
of  the  crank  causes  the  teeth  of  the  compound  gear  CG  to  engage 
in  the  teeth  of  the  translating  rack  tr  cut  hi  a  slotted  sector  of  the 
block.  The  block  is  thereby  caused  to  slide  to  the  rear  on  to  the 
tray  T,  the  guide  rails  of  the  tray  engaging  in  the  grooves  g  g  in 
the  block.  When  the  block  is  sufficiently  withdrawn  the  bottom 
of  the  block  depresses  the  rear  end  of  the  tray  latch  L  and  lifts 
the  forward  end  of  the  latch  out  of  the  catch  A,  where  it  has  been 
held  by  the  pressure  of  the  spring  s.  The  tray  is  now  unlocked 
from  the  breech.  The  upper  front  toe  of  the  latch  L  engages 
in  a  groove  in  the  breech  block,  locking  the  block  and  tray 
together.  The  further  action  of  the  compound  gear  on  the  last 
teeth  of  the  translating  rack  tr  then  causes  the  tray  to  swing  to  the 
right  about  the  hinge  pin,  carrying  the  block  clear  of  the  breech. 
As  the  tray  swings  clear  of  the  breech  the  locking  bolt  Ib  forces 
forward  the  operating  stud  os  and  enters  a  seat  in  the  latch.  The 
latch  is  thus  locked  in  its  raised  position  and  secures  the  breech 
block  against  being  pushed  forward  off  the  tray  when  open. 

In  closing  the  breech  the  operations  are  reversed  hi  order. 
When  the  tray  comes  in  contact  with  the  face  of  the  breech  the 
operating  stud  os  forces  the  locking  bolt  Ib  from  its  seat  in  the 
latch.  The  latch  is  depressed  by  the  spring  s  and  thus  unlocks 
the  block  from  the  tray. 


258 


ORDNANCE  AND  GUXNERY. 


The  two  plugs  shown  in  the  obturator  head  of  the  breech 
mechanism,  Fig.  74,  are  in  the  seats  provided  for  the  insertion  of 
pressure  gauges  when  it  is  desired  to  measure  the  pressure  in  the 
gun: 

In  recent  mechanisms  of  this  type  there  is  added  a  locking 
device  which  locks  the  block  in  position  when  closed  and  insures 
against  the  opening  of  the  block  by  the  pressure  of  the  powder 
gases.  The  locking  bolt  is  withdrawn  by  hand  before  opening 
the  block. 

152.  Bofors  Breech  Mechanism. — The  mechanism  shown  in 
Figs.  75  to  78,  known  as  the  Bofors  breech  mechanism,  is  most 
suitable  for  guns  of  medium  caliber.  It  is  applied  to  the  6-inch 
gun  in  our  service.  The  block,  6  Fig.  75,  is  ogival  in  shape  and 


FIG.  75. 

has  six  threaded  and  six  slotted  sectors.  With  the  ogival  shape 
a  very  small  retraction  to  the  rear  is  necessary  before  the  block 
may  be  swung  open.  In  the  6-inch  gun  this  retraction  is  1.2 
inches,  just  sufficient  to  withdraw  the  obturator  o  from  its  seat 
in  the  bore.  The  block  is  supported  when  the  breech  is  opened  by 
the  block  carrier  c  provided  with  a  central  tube  which  embraces 
a  spindle  s  formed  in  the  block. 


FIG.  73.— Closed. 


FIG.  74.— Open. 
BREECH  MECHANISM  FOR  HEAVY  GUNS. 


FIG.  76.— Closed. 


FIG.  77.— Block  Unlocked,  Ready 
to  Swing  Open. 


FIG.  78.— Open. 
BOFORS  RAPID  FIRE  BREECH  MECHANISM. 


GUNS.  259 

This  mechanism  is  not  applicable  to  the  larger  guns  because 
the  greater  weight  of  the  breech  blocks  in  these  guns  requires 
better  support  than  can  be  conveniently  given  by  this  method. 

The  mechanism  is  actuated  by  means  of  the  lever  /,  Fig.  76, 
which  is  attached  to  the  lower  end  of  the  hinge  pin.  A  spool  p 
mounted  on  the  hinge  pin  has  teeth  cut  near  its  lower  end  which 
engage  in  the  rack  r.  The  rack  slides  in  a  horizontal  groove  cut 
in  the  block  carrier  c,  and  the  teeth  at  its  left  mesh  with  corre- 
sponding teeth  on  the  hub  of  the  breech  block  which  projects 
through  the  rear  face  of  the  carrier. 

When  rotation  of  the  block  is  completed  a  lug,  u  Fig.  75,  on 
the  spool  engages  in  a  slot  at  the  rear  end  of  the  block  and  trans- 
lates the  block  slightly  to  the  rear.  Before  this  translation  is 
complete  the  block  carrier  is  unlocked  from  the  gun,  and  swings  to 


FIG.  79. 

the  rear  with  the  block,  fully  uncovering  the  bore.  The  loading 
tray,  shown  in  Fig.  78,  the  purpose  of  which  is  to  protect  the 
threads  of  the  breech  from  injury  as  the  shot  is  put  into  the  bore, 
remains  permanently  in  the  breech.  When  the  block  is  entered 
and  rotated  the  tray  is  pushed  aside  by  the  threads  on  the  block 
until  it  covers  the  slotted  sector.  On  opening  the  block  it  is 
brought  back  into  the  position  shown. 

In  the  breech  mechanism  shown  in  Fig.  74  the  loading  tray  is 
a  separate  piece  placed  in  the  breech  by  hand  when  loading,  and 
removed  before  closing  the  block. 

153.  The  Welin  Breech  Block. — The  Welin  breech  block, 
largely  used  in  naval  ordnance,  has  the  threaded  sectors  arranged 
in  steps  at  different  distances  from  the  center  of  rotation,  as  shown 


260  ORDNANCE  AND  GUNNERY. 

in  Figs.  79  and  80.     By  this  means  the  threaded  area  may  cover 

two  thirds,  three  fourths,  or  even  a 
larger  portion  of  the  surface  of  the 
block.  A  large  increase  in  threaded 
area  is  thus  secured  over  that  obtained 
on  a  cylindrical  block  with  alternate 
threaded  sectors,  and  the  block  may 
therefore  be  made  smaller.  The  amount 
of  rotation  required  in  locking  and  un- 
locking is  also  diminished,  one  twelfth 
of  a  turn  sufficing  for  the  block  shown 
in  Fig.  79,  and  one  sixteenth  for  the 
block  of  Fig.  80. 

Obturation. — There  must  be  provided  at  the  breech  of  the 
gun  some  device  that  will  prevent  the  powder  gases  from  passing 
to  the  rear  into  the  threads  and  other  parts  of  the  breech  mechan- 
ism. If  any  passage  is  open  to  the  gases  they  are  forced  through 
it  with  great  velocity  by  the  high  pressure  existing  in  the  bore. 
Their  velocity  together  with  their  high  temperature  gives  to  them 
great  erosive  power,  and  the  threads  and  other  parts  of  the  breech 
mechanism  subject  to  their  action  are  eroded,  channeled,  and 
worn  away  to  such  an  extent  that  the  breech  mechanism  is  soon 
ruined  and  the  gun  is  rendered  useless. 

In  guns  that  use  fixed  ammunition  the  obturation  is  performed 
by  the  cartridge  case,  which  expands  under  the  pressure  in  the 
bore  to  a  tight  fit  against  the  walls  of  the  gun.  The  breech  mechan- 
ism of  these  guns  contains,  therefore,  no  obturator  parts. 

With  the  slotted  screw  breech  block  two  systems  of  obturation 
are  used.  They  are  known  by  the  names  of  their  inventors, 
DeBange  and  Freyre. 

154.  The  DeBange  Obturator. — This  system  is  in  the  most 
general  use.  It  is  seen  at  o,  Figs.  72  and  75,  in  the  breech  mechan- 
isms already  described.  The  details  are  shown  in  Fig.  81.  The 
obturator  consists  of  the  steel  mushroom  head  h  with  the  spindle 
s,  the  pad  p,  the  split  steel  rings  r,  and  the  steel  filling-in  disk  d. 
The  pad  p  is  made  of  asbestos,  tallow,  and  paraffine  or  other 
substance,  that  together  form  a  plastic  mixture  that  melts  only 
at  a  high  heat.  The  ingredients  are  mixed  and  then  pressed  into 


GUNS. 


201 


shape  under  a  hydraulic  press  and  protected  by  a  cover  made  of 
canvas  or  of  asbestos  wire  cloth.    The  split  rings,  r  Fig.  81  and 


TUBE. 


FIG.  81. 

Fig.  82,  are  hardened,  and  their  outer  surfaces,  which  are  coned 
toward  the  front,  are  very  care- 
fully ground,  so  that  their  diameters 
when  the  rings  are  free  are  0.01 
of  an  inch  larger  than  the  diam- 
eters of  the  conical  seat  in  the 
bore.  The  edges  of  the  rings 
therefore  always  bear  against  the 
walls  of  the  bore. 

The  pressure  of  the  gases 
against  the  mushroom  head  com- 
presses the  elastic  pad  and  further 
presses  the  split  rings  against  the 
walls  of  the  bore,  thus  effectually  preventing  the  passage  of  gas 
to  the  rear. 

The  smaller  split  ring  surrounding  the  spindle  serves  to  pre- 


FIG.  82. 


262 


ORDNANCE  AND  GUNNERY. 


vent  escape  of  the  pad  composition  between  the  filling-in  disk  and 
the  spindle. 

The  spindle  s  passes  through  a  central  hole  in  the  breech 
block.  The  obturator  parts  are  held  in  place  by  the  split  nut  n 
clamped  on  the  spindle.  The  nut  bears  against  a  shoulder  in  the 
block  through  the  ball  bearing  6.  It  will  be  seen  that  the  breech 
block  may  rotate  independently  of  the  obturator  parts,  so  that 
in  opening  the  breech  the  rotation  of  the  block  is  not  affected  by 
any  sticking  of  the  obturator  to  its  seat  in  the  gun.  On  retraction 
of  the  block  the  obturator  is  readily  withdrawn  from  its  conical 
seat. 

A  vent  is  drilled  the  full  length  of  the  obturator  spindle  to 
afford  a  passage  for  the  flames  from  the  primer  to  the  powder 
charge  in  the  gun.  The  two  grooves  at  the  rear  end  of  the  spindle 
serve  for  the  attachment  of  the  firing  mechanism. 

The  Freyre  Obturator. — The  Freyre  obturator  shown  in  Fig. 
83  is  used  in  the  3.6  inch  field  mortar.  The  head  g  is  cone  shaped. 


FIG.  83. 

In  rear  of  it  resting  against  the  head  of  the  breech  block  h  is 
the  cone  shaped  steel  ring  /.  The  head  g  is  constantly  pressed 
forward  by  the  spring  e.  Under  the  action  of  the  powder  pressure 
the  head  is  forced  to  the  rear  and  expands  the  ring  /  against  the 
walls  of  the  bore. 

With  this  obturator  the  breech  mechanism  is  comparatively 
short  and  light  in  weight,  which  is  an  important  advantage  in  a 


GUXS. 


263 


field  mortar.  The  obturator  ring  with  its  thin  front  edge  is,  how- 
ever, readily  subject  to  accidental  injury,  which  would  render  the 
obturation  imperfect. 

155.  Firing  Mechanism. — A  seat  for  the  firing  mechanism  is 
formed  on  the  rear  end  of  the  obturator  spindle  by  two  grooves,  g 
Fig.  84,  cut  in  the  spindle.  A  hinged  collar  k  embraces  the  end  of 
the  spindle.  The  housing  h  screws  over  the  collar  and  is  locked 


FIG.  84. 

to  it  by  the  spring  pin  p.  The  ejector  e  pivoted  in  the  housing 
has  at  its  lower  end  a  forked  seat  for  the  head  of  the  primer. 
Projecting  ribs  on  the  front  face  of  the  housing  form  guides  for 
the  slide,  d  Fig.  84  and  Fig.  85.  The  slide  is  moved  up  or  down 
by  means  of  the  handle  6,  the  catch  lever  a  being  first  pressed  to 
release  a  holding  catch.  Pivoted  at  o  in  the  slide  is  the  slotted 
firing  leaf  I,  which  carries  the  insulated  brass  contact  clip  c  and 
is  provided  with  an  eye  into  which  the  hook  of  the  lanyard 
engages. 


264  ORDNANCE  AND  GUNNERY. 

The  slide  being  at  its  uppermost  position,  the  primer  r  is  inserted 
in  the  vent  in  the  obturator  spindle,  the  head  of  the  primer  resting 
in  its  seat  in  the  ejector.  The  slide  is  then  pushed  down.  The 
firing  leaf  I,  by  means  of  the  slot,  embraces  the  insulated  primer 
wire  just  in  front  of  the  button  at  its  outer  end.  The  two  halves 
of  the  contact  clip  c  spring  apart  and  embrace  the  uninsulated 
button. 

If  the  breech  is  closed,  a  pull  on  the  lanyard  rotates  the  firing 
leaf  I  about  its  axis  o,  drawing  out  the  primer  wire  and  firing  the 
primer  by  friction;  or  the  closing  of  the  electric  circuit,  which 
enters  the  mechanism  through  the  electric  terminal  n,  will  fire 
the  primer  electrically.  The  electric  current  passes  through 
insulated  parts  to  the  platinum  firing  bridge  inside  the  primer 
and  thence  through  the  body  of  the  primer  to  the  metal  of  the 
gun  and  to  the  ground. 

Firing  by  either  of  these  methods  cannot  be  accomplished 
unless  the  slide  d  is  all  the  way  down  and  the  breech  is  fully  closed. 

A  safety  lug  on  the  right  side  of  the  housing  engages  in  a 
groove  in  the  firing  leaf  and  prevents  the  latter  being  drawn  to 
the  rear  before  the  slide  is  all  the  way  down.  The  contact  clip 
engages  the  primer  button  only  in  the  last  part  of  the  downward 
movement  of  the  slide. 

The  inner  end  of  the  safety  bar,  s  Fig.  85,  also  engages  the 
firing  leaf.  The  outer  end  of  the  safety  bar  embraces  a  stud  pro- 
jecting from  the  safety  bar  slide,  i  Fig.  87,  and  the  safety  bar  slide 
carries  at  its  outer  end  a  stud  that  engages  in  a  groove  cut  in  the 
gun.  The  groove  is  so  shaped  as  to  withdraw  the  safety  bar  only 
at  the  last  part  of  the  movement  of  the  block  in  closing.  At  this 
moment  also  the  parts  of  the  electric  circuit  breaker,  fixed  one  to 
the  block  and  the  other  to  the  gun,  Fig.  87,  come  into  contact. 

It  will  be  seen  therefore  that  the  primer  cannot  be  fired  until 
the  breech  block  is  locked. 

We  have  seen  that  the  breech  block  rotates  independently  of 
the  obturator  spindle.  In  order  then  that  the  firing  mechanism 
may  always  be  in  an  upright  position  when  the  breech  is  closed,  a 
guide  bar,  m  Fig.  87,  fixed  at  one  end  to  the  housing  and  at  the 
other  end  to  the  block,  causes  the  mechanism  to  rotate  on  the 
spindle  with  the  block. 


FIG.  85.— Slide  Raised  and 
Primer  Inserted. 


FIG.  86. — S'.ide  Lowered  Ready 
for  Firing. 


FIG.  87.— Breech  Partially  Unlocked.     Safety  Bar  Forced  in  by  Cam  Slot, 
and  Electric  Circuit  Broken. 


FIRING  MECHANISM  FOR  HEAVY  GUNS. 


GUNS. 


265 


The  fired  primer  is  ejected  by  lifting  the  slide.  The  lug  on  the 
slide,  d  Fig.  84,  strikes  the  upper  part  of  the  ejector  lever,  giving 
to  the  lower  end  a  sharp  movement  to  the  rear,  which  throws  the 
primer  clear  of  the  piece. 

156.  Sliding  Wedge  Breech  Mechanism. — The  method  of 
closing  the  breech  by  means  of  a  sliding  wedge-shaped  block  is 
used  principally  by  Krupp,  and 
to  some  extent  by  other  makers. 
The  jacket  of  the  gun,  a  Fig.  88, 
extends  to  the  rear  of  the  tube,  and 
the  bore  of  the  gun  is  continued 
through  the  extension.  A  slot 
cut  transversely  through  the  jacket 
just  in  rear  of  the  tube  forms  a 
seat  for  the  sliding  breech  block 
k.  The  front  surface  of  the  slot 
is  a  plane  surface  perpendicular 
to  the  axis  of  the  bore,  the  rear 
surface  is  cylindrical  and  inclined 
to  the  axis  of  the  bore.  Two 
guides  b  b'  similarly  inclined  guide 
the  breech  block  in  its  movements. 
The  breech  block  is  of  the  same 
shape  as  the  slot  and  slides  in  and 
out  to  close  and  open  the  breech. 
The  greater  part  of  the  movement 
of  the  block  is  accomplished 
rapidly  by  means  of  the  transla- 
ting screw  c,  which  is  held  in  two 
bearings  at  the  ends  of  the  block 
and  works  in  a  half  nut  d  on  the 

gun.  The  screw  is  turned  by  means  of  the  handle  e,  which  is 
removed  from  the  position  in  which  it  is  shown  and  applied  to  the 
end  of  the  screw  c.  The  final  movement  in  closing  and  the  initial 
movement  in  opening  are  effected  more  slowly  and  more  power- 
fully by  the  locking  screw  g.  A  nut  /  carried  on  the  locking  screw 
locks  the  block  when  closed. 

Obturation. — Obturation   is   effected  with   the   sliding   breech 


FIG. 


266 


ORDNANCE  AND  GUNNERY. 


BREECH 

BLOCK. 

i 

TL 

BE 
-C 

V 

6 

SI 

a 

e 

6 

H^ 

i 

d 

1 

1 

FIG.  89. 


block  by  means  of  a  steel  obturator  plate,  6  Fig.  89,  carried  in  the 

block,  and  a  steel  cup-shaped  ring,  a, 
called  the  Broadwell  ring,  seated  in  the 
end  of  the  bore.  The  pressure  of  the 
gases  forces  the  ring  back  tightly 
against  the  plate  and  at  the  same  time 
presses  the  thin  lip  c  against  the  walls 
of  the  bore.  The  grooves  shown  in  the 
rear  surface  of  the  ring  serve  as  air 
packing  and  also  to  collect  any  dirt  that 
may  be  on  the  surface  of  the  plate.  The 
hollow  e  in  the  plate  also  serves  to 
collect  fouling  and  to  remove  it 
from  the  bearing  surface.  The  plate 
is  forced  tightly  against  the  ring  by 
the  last  movement  of  the  locking 
screw  in  closing. 

This  mechanism  is  better  adapted  to  small  than  to  large  guns. 
The  light  breech  block  of  a  small  gun  may  be  pushed  to  its  seat  by 
hand.  Only  a  limited  screw  motion  is  then  necessary  to  firmly 
seat  and  lock  the  block.  Better  obturation  is  also  obtained  when 
a  cartridge  case  is  used  with  this  mechanism  than  when  dependence 
is  placed  on  the  Broadwell  ring. 

In  guns  using  fixed  ammunition,  if  the  breech  block  closes  from 
the  rear  less  care  is  required  in  inserting  the  round  than  if  the 
breech  is  closed  from  one  side.  In  the  latter  case  if  the  round  is 
not  sufficiently  inserted,  the  block  in  closing  strikes  the  cartridge 
case  and  a  temporary  jamming  of  the  mechanism  occurs. 

157.  Older  Forms  of  Breech  Mechanism. — There  are  mounted 
in  our  fortifications  many  guns  equipped  with  the  breech  mechan- 
ism shown  in  Fig.  90. 

The  block  is  revolved  by  means  of  one  crank  fixed  to  the  gun, 
and  withdrawn  and  swung  aside  by  a  second  crank  attached  to 
the  tray.  The  shaft  of  the  revolving  crank  carries  at  its  end  the 
pinion  p,  Fig.  91,  which  works  in  the  rack  of  the  rotating  ring  b. 
The  rotating  ring  revolves  in  bearings  provided  in  the  face  plate, 
and  communicates  its  motion  of  rotation  to  the  block  through  the 
lug  a,  which  engages  in  one  of  the  slotted  sectors.  When  the  rota- 


GUNS. 


267 


tion  of  the  block  is  completed  the  translating  stud  at  the  bottom 
of  the  block  has  entered  one  of  the  threads  of  the  double  threaded 
translating  roller.  The  other  thread  of  the  roller  works  in  a 
corresponding  thread  cut  in  the  tray.  Rotation  of  the  translating 


FIG.  90. 


crank  causes  the  block  to  move  to  the  rear  with  a  movement 
equal  to  the  sum  of  the  movements  due  to  each  of  the  two 
threads.  When  the  front  of  the  roller  passes  to  the  rear  of 
the  stud  shown  acting  on  the  tray  latch,  the  block  is  brought 


268 


ORDNANCE  AND  GUNNERY. 


to  a  stop  on  the  tray,  and  the  shock  of  its  arrest  is  sufficient 
to  release  the  tray  latch  from  its  hold  on  the  lip  of  the  recess  in 

the  gun.  The  tray  then  swings 
aside,  carrying  the  block  clear 
of  the  breech. 

The  tray  is  similar  in  general 
shape  to  the  tray  of  the  more 
modern  mechanism  shown  in 
Fig.  72. 

1 2 -inch  Mortar  Breech 
Mechanism. — The  12-inch  mor- 
tars are  provided  with  the 
mechanism  shown  in  Fig.  92. 
It  differs  from  the  mechanism 
just  described  only  in  the 
method  of  rotating  the  breech 
block.  A  steel  plate  k  is 
fixed  to  the  rear  face  of  the 

breech  block  and  extending  upwards  provides  journals  for  the 
pinions  a,  b,  and  c  of  the  rotating  gear.  The  pinion  c  meshes  in 
the  rack  e  fixed  to  the  gun,  and  when  the  crank  d  is  turned  the 


FIG.  91. 


FIG.  92. 


block  is  rotated  to  open  or  close.  The  block  is  withdrawn  on  a 
tray  as  described  above.  The  translating  stud  that  engages  in 
the  translating  roller  is  seen  at  the  bottom  of  the  block. 


GUNS.  269 

The  vent  shield  /,  cut  shorter  than  shown  in  the  figure,  is  pro- 
vided with  a  stud  at  its  lower  end  that  engages  with  the  safety 
bar  of  the  firing  mechanism  already  described.  The  stud  at  its 
upper  end  works  in  the  groove  g  cut  in  the  gun,  withdrawing  the 
safety  bar  as  the  breech  is  fully  closed. 

Automatic  and  Semi-automatic  Breech  Mechanisms. — In 
guns  provided  with  automatic  breech  mechanism  the  energy  of 
recoil  or  the  pressure  of  the  powder  gases  is  utilized  to  open  the 
breech,  withdraw  the  fired  shell,  insert  a  new  cartridge  and  close 
the  breech.  After  the  firing  of  the  first  round  the  only  operation 
necessary  for  firing  the  succeeding  rounds  is  pulling  the  trigger. 
The  automatic  mechanism  is  at  present  applied  only  to  guns  of 
small  caliber  that  use  the  small  arm  cartridge  or  fire  a  projectile 
weighing  not  more  than  a  pound. 

The  semi-automatic  mechanism  is  applied  to  guns  of  medium 
caliber,  up  to  6  inches,  and  efforts  are  being  made  to  adapt  it  to 
the  larger  guns.  The  breech  is  opened  by  mechanism  that  is 
operated  during  the  recoil  or  counter  recoil  of  the  piece,  and  if 
fixed  ammunition  is  used  the  fired  shell  is  ejected.  At  the  same 
time  power  is  stored  in  a  spring  to  be  later  used  in  closing  the  breech. 

In  some  mechanisms  the  insertion  of  the  succeeding  round 
by  hand  operates  the  breech  closing  mechanism.  In  others  the 
pulling  of  a  lever  after  the  insertion  of  the  round  actuates  this 
mechanism. 

158.  THE  2.38-iNCH  FIELD  GUN  BREECH  MECHANISM. — The 
semi-automatic  breech  mechanism  of  the  2.38-inch  light  field  gun 
is  shown  in  Figs.  93  to  95. 

The  wedge  shaped  breech  block  6  is  seated  in  a  vertical  slot 
cut  through  the  extension  of  the  jacket.  Projecting  guide  ribs,  t 
Fig.  94,  in  the  slot  engage  in  grooves  cut  in  the  sides  of  the  block. 
The  block  is  lowered  or  raised  to  open  or  close  the  breech  by  means 
of  the  crank  c.  A  stud  at  the  end  of  the  crank  engages  in  the  cam 
groove  g  on  the  right  side  of  block,  the  groove  being  so  shaped 
that  the  crank  gives  vertical  movement  to  the  block.  On  the 
outer  end  of  the  crank  shaft  is  the  operating  lever,  I  Fig.  95,  attached 
to  which  is  the  operating  bar  r,  and  the  coiled  operating  spring. 

The  forward  end  of  the  operating  bar  embraces  the  pin  pro- 
truding from  the  sliding  piece  s,  which  slides  in  an  undercut  groove 


270 


ORDNANCE  AND  GUNNERY. 


FIG.  93. 


C 


2.38-inch  Field  Gun,  Semi-automatic  Breech  Mechanism. 


GUNS.  271 

v  in  the  locking  ring  of  the  piece.  The  pawl  p,  pivoted  on  the  same 
pin,  has  at  its  upper  end  a  stud  which  rests  on  a  shoulder  above 
the  groove.  The  end  of  a  spring  pin,  e,  in  the  pawl  works  in  a 
slot  cut  in  the  sliding  piece  s  and  limits  the  motion  of  the  pawl. 

The  mechanism  above  described  is  fixed  to  the  piece  and 
moves  with  the  piece  in  recoil. 

A  stud,  d,  is  fixed  on  the  recoil  cylinder  of  the  carriage.  When 
the  piece  recoils,  carrying  the  mechanism  with  it,  the  pawl  p  is 
lifted  by  the  stud  and  falls  back  into  the  position  shown  as  soon 
as  it  has  passed  the  stud.  As  the  piece  returns  in  counter  recoil 
the  pawl  is  engaged  by  the  stud  and  held.  The  piece  continues 
its  forward  movement.  The  slide  s  moves,  relatively,  to  the  rear 
in  its  slot,  causing  the  bar  r  to  rotate  the  operating  lever  I  against 
the  tension  of  the  coiled  spring. 

The  rotation  of  the  lever  lowers  the  breech  block  and  opens 
the  breech.  The  block  in  the  last  part  of  its  movement  oper- 
ates the  forked  extractor  x  which  ejects  the  empty  cartridge 
case. 

The  stud  on  the  upper  end  of  the  pawl  p  has  now  moved  up 
the  incline  at  the  rear  end  of  the  shoulder  on  which  it  slides,  lift- 
ing the  pawl,  disengaging  it  from  the  stud  d  on  the  carriage,  and 
allowing  the  piece  to  finish  its  movement  into  battery.  The  pawl 
p  being  disengaged  from  the  stud  the  breech  block  moves  upward 
under  the  action  of  the  operating  spring  until  the  curved  locking 
studs  o  on  each  arm  of  the  extractor,  Fig.  94,  engage  in  the  cor- 
responding recesses  cut  in  the  sides  of  the  block.  The  curved 
shape  of  the  locking  studs  and  recesses,  together  with  the  direc- 
tions in  which  the  engaging  parts  are  constrained  to  move,  prevent 
further  movement  of  the  parts  and  the  block  is  therefore  locked 
open  against  the  tension  of  the  operating  spring. 

The  rear  part  of  the  jacket  extension  is  trough  shaped  to  permit 
the  ready  insertion  of  the  cartridge  into  the  breech.  As  the 
cartridge  is  pushed  into  the  breech  writh  force  its  flanged  head 
engages  the  extractor  arms  and  forces  the  locking  studs  o  out  of 
the  recesses.  The  action  of  the  operating  spring  through  the 
lever  I  and  the  crank  c  then  lifts  the  block  and  closes  the  breech. 

The  firing  mechanism  is  similar  to  that  of  the  3-inch  field  gun 
which  is  fully  described  in  Chapter  VIII. 


272 


ORDNANCE  AND  GUNNERY. 


159.  THE  3-iNCH  SEACOAST  GUN  BREECH  MECHANISM. — The 
operating  parts  of  the  U.  S.  Ordnance  Co.'s  semi-automatic  breech 
mechanism,  applied  to  the  3-inch  seacoast  gun,  are  shown  in  Figs. 
96  and  97.  Attached  to  the  gun  is  the  actuating  rod  a,  its  front 


FIG.  96. 

end  provided  with  three  twisted  ribs  which  are  practically  screw 
threads  with  a  very  long  pitch.  The  nut  n  similarly  threaded 
is  held  in  the  bearing  b  which  is  fixed  on  the  recoil  cylinder  c  of 
the  carriage. 


FIG.  97. 

When  the  gun  recoils  the  nut  n  is  turned  through  128  degrees 
by  the  actuating  rod,  but  in  counter  recoil  the  nut  is  held  by  a 
pawl  and  the  actuating  rod  turns  clockwise,  looking  from  the 
rear,  in  passing  through  the  nut.  The  turning  of  the  actuating 
rod  operates  the  miter  gears  at  its  rear  end  and  through  them 
opens  the  breech  and  ejects  the  fired  shell. 


GUNS.  273 

The  operating  spring,  one  end  of  which  is  held  in  the  adjusting 
nut  d  which  is  carried  in  a  bearing  on  the  gun,  is  wound  up  by 
the  movement  of  the  actuating  rod  during  counter  recoil,  and  the 
energy  stored  in  the  spring  is  later  utilized  to  close  the  breech. 
A  small  hydraulic  buffer,  /,  modifies  the  action  of  the  spring  and 
relieves  the  mechanism  of  violent  shock.  The  block  is  held  open 
by  the  lug  I,  which  under  the  action  of  a  spring  falls  inside  the 
carrier  when  the  breech  is  open. 

After  the  insertion  of  the  cartridge,  hand  pressure  on  the  trip- 
ping lever  t  lifts  the  lug  I  from  inside  the  carrier.  The  operating 
spring,  then  free  to  act,  closes  the  breech  block. 

The  firing  mechanism  is  similar  to  that  described  in  Chapter 
VIII  in  the  3-inch  field  gun.  The  trigger  is  seen  at  r,  Fig.  97. 

Automatic  breech  mechanisms  are  described  in  Chapter  XVI, 
in  the  descriptions  of  the  guns  in  which  they  are  used. 


CHAPTER  VII. 
RECOIL   AND   RECOIL   BRAKES. 

1  60.  Stresses  on  the  Gun  Carriage.  —  The  stresses  to  which  a 
gun  carriage  is  subjected  are  due  to  the  action  of  the  powder  gases 
on  the  piece.  Gun  carriages  are  constructed  either  to  hold  the 
piece  without  recoil  or  to  limit  the  recoil  to  a  certain  convenient 
length.  In  the  first  case  the  maximum  stress  on  the  carriage  is 
readily  deduced  from  the  maximum  pressure  in  the  gun.  In  the 
second  case  it  becomes  necessary  to  determine  all  the  circum- 
stances of  recoil  in  order  that  the  force  acting  at  each  instant  may 
be  known,  and  the  parts  of  the  carriage  designed  to  withstand 
this  force  and  to  absorb  the  recoil  in  the  desired  length. 

Velocity  of  Free  Recoil.  —  Suppose  the  gun  to  be  so  mounted 
that  it  may  recoil  horizontally  and  without  resistance.  On  ex- 
plosion of  the  charge  the  parts  of  the  system  acted  upon  by  the 
powder  gases  are  the  gun,  the  projectile,  and  the  powder  charge 
itself,  the  latter  including  at  any  instant  both  the  unburned  and 
the  gaseous  portions.  While  the  projectile  is  in  the  bore,  if  we 
neglect  the  resistance  of  the  air,  none  of  the  energy  of  the  powder 
gases  is  expended  outside  the  system.  The  center  of  gravity  of  the 
system  is  therefore  fixed  and  the  sum  of  the  quantities  of  motion 
in  the  different  parts  is  zero.  The  movement  of  the  powder  gases 
will  be  principally  in  the  direction  of  the  projectile.  We  may 
therefore  write 

(1) 


in  which  M,  m,  and  ,«  are  the  masses  of  the  gun,  projectile,  and 
charge  of  powder,  respectively;   and  vf,  v,  and  vc  the  velocities  of 

274 


RECOIL  AND  RECOIL  BRAKES.  275 

the  same  parts.  The  mass  of  the  charge  is  the  same  whether  the 
charge  is  unburned  or  partially  or  wholly  burned. 

The  velocity  of  the  projectile  at  any  point  in  the  bore  of  the 
gun  may  be  determined  from  the  formulas  of  interior  ballistics, 
equations  (112)  to  (115),  page  100.  The  velocity  of  the  center 
of  mass  of  the  products  of  combustion  is  unknown.  The  velocity 
of  the  products  varies  from  zero  near  the  breech  to  v  at  the  base 
of  the  projectile,  and  we  may,  without  material  error,  consider 
the  velocity  of  the  center  of  mass  of  the  products  as  equal  to  half 
the  velocity  of  the  projectile. 

Writing  v/2  forvcin  equation  (1),  replacing  masses  by  weights, 
and  solving  for  vf  we  obtain 

W+^(I) 

vt=~W~v 

W,  w,  and  a>  being  the  weights  of  the  gun,  projectile,  and  charge. 

At  the  muzzle  of  the  gun  v  becomes  the  initial  velocity  V,  and 
for  the  velocity  of  free  recoil  at  that  instant 


(3) 


This  value  v/  is  not  the  maximum  velocity  of  free  recoil, 
though  it  is  the  maximum  value  reached  while  the  velocities  of 
the  gun  and  of  the  projectile  are  connected.  At  the  departure  of 
the  projectile  the  bore  of  the  gun  is  still  filled  with  gases  under 
tension,  which  continue  to  exert  pressure  on  the  breech  and  in- 
crease the  velocity  of  recoil.  The  value  v/  obtained  by  the  above 
equation  is  about  7/10  of  the  maximum  velocity  of  free  recoil. 

It  has  been  determined  by  experiment  with  the  Sebert  veloci- 
meter  that  the  maximum  velocity  of  free  recoil  may  be  obtained 
from  equation  (3)  by  substituting  for  the  quantity  %u>V  the  quan- 
tity 4700cD.  The  equation  then  becomes 


being  the  maximum  velocity  of  free  recoil. 


276  ORDNANCE  AND  GUNNERY. 

The  coefficient  4700  applies  to  smokeless  powders.  The  co- 
efficient for  black  powders  was  3000. 

161.  Determination  of  the  Circumstances  of  Free  Recoil.— 

In  the  above  equations  the  velocity  of  free  recoil  is  expressed  as  a 
function  of  the  velocity  of  the  projectile,  and  we  have  in  the  bal- 
listic formulas 'the  velocity  of  the  projectile  expressed  as  a  func- 
tion of  the  travel  of  the  projectile.  We  might  therefore  now 
determine  the  velocity  of  free  recoil  as  a  function  of  the  travel  of 
the  projectile.  But  in  the  determination  of  all  the  circumstances 
of  recoil  it  is  necessary  to  know  the  relations  between  the  velocity, 
time,  and  length  of  recoil ;  and  in  order  to  arrive  at  these  relations 
by  means  of  equation  (2),  we  must  obtain  an  expression  for  the 
velocity  of  the  projectile  as  a  function  of  the  time. 

With  the  velocity  of  the  projectile  expressed  as  a  function  of 
the  time,  equation  (2)  will  then  express  the  velocity  of  free  recoil 
as  a  function  of  the  time,  and  with  the  velocity  of  recoil  so  ex- 
pressed we  may  obtain  the  length  of  recoil  from  the  equation 


x  =  /  Vfdt  (5) 

x  representing  the  length  of  free  recoil. 

We  thus  obtain  the  complete  relations  between  the  velocity, 
time,  and  length  of  free  recoil. 

162.  Velocity  of  the  Projectile  as  a  Function  of  the  Time.— 
The  velocity  of  the  projectile  as  a  function  of  the  time  is  obtained 
in  the  following  manner.  Representing  the  travel  of  the  pro- 
jectile by  u,  we  have 

v  =  du/dt,     from  which     t=   I  —  du  (6) 

That  is,  t  is  the  area  under  the  curve  whose  ordinates  are  values 
of  l/v  and  whose  abscissas  are  values  of  u. 

Therefore  if  we  construct  such  a  curve  the  area  under  the 
curve  from  the  origin  to  any  ordinate  will- be  the  time  correspond- 
ing to  the  velocity  whose  reciprocal  is  represented  by  the  ordinate. 

Construct  the  curve  v,  Fig.  98,  from  the  ballistic  formulas, 
the  abscissas  representing  travel,  the  ordinates  velocity  of  the 
projectile. 


RECOIL  AND  RECOIL  BRAKES. 


277 


Take  the  value  of  v  as  expressed  by  any  ordinate  and  lay  off 
its  reciprocal  on  the  same  ordinate,  to  any  convenient  scale.  The 
curve  l/i?  hi  the  figure  is  obtained  in  this  way.  Its  ordinates  are 
values  of  l/v,  its  abscissas  are  values  of  u.  The  areas  under  the 
curve  are  therefore  values  of  t,  equation  (6). 

For  very  small  values  of  v  the  ordinates  1/v  will  be  very  large 
and  will  not  fall  within  the  limits  of  an  ordinary  drawing.  We 
cannot  determine,  then,  from  the  drawing,  the  area  under  the  first 
part  of  the  curve.  But  we  can  obtain  a  sufficiently  close  approxi- 
mation to  this  area  in  the  following  manner.  We  may  assume, 


FIG.  98. 


Multiplying  by  dt  and  integrating,  we  have,  since  J  v  dt  =  u, 


without  material  error  in  the  determination  of  this  small  area, 
that  the  velocity  of  the  projectile  as  a  function  of  the  time  is  ex- 
pressed by  the  equation  of  a  parabola 

(7) 


(8) 


At  the  instant  at  which  the  shot  leaves  the  bore,  v  in  equation 
(7)  becomes  the  initial  velocity  V,  and  denoting  the  corresponding 
time  by  i'  we  obtain  from  that  equation 


or 


273  ORDNANCE  AND  GUNNERY. 

Substituting  this  value  of  (2p)*  in  equation  (8),  t  in  that  equa- 
tion becoming  t'  and  u  the  total  travel  of  the  projectile  U,  we 
obtain 

e=^*L 

~2  V 

t'  is  then  the  total  area  under  the  curve  1/v,  Fig.  98,  and  sub- 
tracting from  t'  the  area  that  can  be  measured  we  obtain  the  area 
under  that  part  of  the  curve  near  the  origin  that  is  not  plotted. 

Having  now  from  the  v  curve  the  values  of  v  =  f(u)  and  from 
the  areas  under  the  1/v  curve  the  values  of  t  =  f(u)  we  may,  by 
combination,  determine  the  desired  values  of  v  =  f(t). 

Using  as  abscissas  the  areas  under  the  curve  1/v,  which  are  the 
values  of  t,  and  as  ordinates  the  corresponding  ordinates  of  the 
v  curve  v,  which  are  the  velocities,  we  obtain  the 

curve  of  the  velocity  of  the  projectile  as  a  function 
of  the  time,  Fig.  99. 

Since  the  velocity  of  free  recoil  as  given  by 
equation  (2)  is  equal  to  the  velocity  of  the  pro- 
jectile multiplied  by  a  constant,  the  curve  in 
Fig.  99  becomes  at  once  the  curve  of  velocity 
of  free  recoil,  if  we  consider  the  scale  of  the 
FIG  99  ordinates  as  multiplied  by  the  coefficient  of  v  in 

equation  (2). 

163.  Maximum  Velocity  of  Free  Recoil. — The  curve  shown 
in  Fig.  99  gives  the  velocity  of  free  recoil  only  while  the  pro- 
jectile is  in  the  bore,  and  as  previously  explained  the  velocity 
of  recoil  has  not  reached  its  maximum  when  the  projectile  leaves 
the  piece.  The  value  of  the  maximum  velocity  of  recoil  is  given 
by  equation  (4).  With  this  value  as  an  ordinate,  Fig.  100,  draw  a 
line  parallel  to  the  axis  of  t  and  continue  the  curve  of  velocity 
already  drawn  until  it  is  tangent  to  this  line.  It  is  reasonable  to 
infer  that  the  rate  of  change  in  the  curvature  of  the  curve  of  recoil 
will  continue  uniform  from  the  point  corresponding  to  the  muzzle 
of  the  gun  to  the  point  of  maximum  velocity,  and  the  curve  so 
continued  will  with  sufficient  exactness  express  the  circumstances 
of  motion.  A  slight  error  made  in  the  selection  of  the  point  of 
tangency  will  be  without  practical  effect  on  the  determinations  to 


RECOIL  AND  RECOIL  BRAKES. 


279 


be  later  made  from  this  curve.  The  abscissa  of  the  point  of  tan- 
gency  is  the  time  corresponding  to  the  maximum  velocity  of  free 
recoil. 

As,  by  assumption,  there  is  no  resistance  to  recoil,  the  maximum 
velocity  attained  will  never  be  reduced,  and  the  curve  will  extend 
indefinitely  parallel  to  the  axis  of  t\ 

The  tangent  to  the  curve  at  any  point  is  a  value  of  dvf/dt,  and 
therefore  represents  the  acceleration  at  the  instant  of  time  repre- 
sented by  the  abscissa  of  the  point.  The  tangent  has  a  maximum 
value  at  the  point  of  inflexion  of  the  curve,  the  point  where  the 
curve  ceases  to  be  convex  toward  the  axis  of  t,  and  becomes  con- 
cave. This  point  is  therefore  the  point  of  maximum  acceleration. 


FIG.  100. 

The  maximum  acceleration  being  due  to  the  maximum  powder 
pressure  in  the  gun  the  abscissa  of  the  point  of  inflexion  is  the  time 
of  the  maximum  pressure. 

Since,  equation  (5),  x  =  fvfdt,  the  area  under  the  curve  vf,  Fig. 
100,  from  the  origin  to  any  ordinate  is  the  length  of  free  recoil 
corresponding  to  the  velocity  represented  by  the  ordinate. 

Retarded  Recoil.— In  the  discussion  thus  far  we  have  neglected 
all  resistances  and  have  considered  the  movement  of  the  gun  in 
recoil  as  unopposed.  When  the  gun  is  mounted  on  a  carriage  the 
recoil  brakes,  of  whatever  character,  begin  to  act  as  soon  as  recoil 
begins,  and  consequently  the  velocity  of  recoil  is  less  at  each  in- 
stant than  the  velocity  shown  by  the  curves  just  determined. 

The  manner  of  obtaining  the  velocity  of  retarded  recoil  will  be 
explained  later. 


280  ORDNANCE  AND  GUNNERY. 

Recoil  Brakes. — To  absorb  the  energy  of  recoil  and  to  bring  the 
gun  to  rest  in  a  convenient  length,  all  gun  carriages  which  permit 
movement  of  the  gun  in  recoil  are  provided  with  recoil  brakes. 

These  are  of  two  general  classes,  friction  brakes  and  fluid  brakes. 
Friction  brakes  were  formerly  used  on  seacoast  carriages,  but  are 
now  confined  exclusively  to  wheeled  carriages.  Fluid  brakes  are 
either  hydraulic  or  pneumatic.  Pneumatic  brakes,  depending 
for  their  resistance  on  the  compression  of  air,  have  been  used  in 
England  to  some  extent  on  seacoast  carriages.  On  account  of  the 
difficulty  of  preventing  loss  of  pressure  in  the  brakes  through 
leakage  of  the  air  these  brakes  are  not  satisfactory. 

164.  Hydraulic  Brakes. — A  hydraulic  recoil  brake  consists  of  a 
cylinder  filled  with  liquid,  and  a  piston.  Relative  movement  is 
given  to  the  cylinder  and  piston  by  the  recoil,  and  provision  is 
made  for  the  passage  of  the  liquid  from  one  side  of  the  head  of  the 
piston  to  the  other  by  apertures  cut  in  the  piston  or  in  the  walls  of 
the  cylinder.  The  power  of  the  brake  lies  in  the  pressure  produced 
in  the  cylinder  by  the  resistance  offered  by  the  liquid  to  motion 
through  the  apertures. 

If  the  area  of  the  apertures  is  constant  it  is  evident  that  the 
resistance  to  flow  will  be  greater  as  the  velocity  of  the  piston  or 
the  velocity  of  recoil  is  greater.  Therefore  the  pressure  in  the 
cylinder,  which  measures  the  resistance  offered,  will  vary  with  the 
different  values  of  the  velocity  of  recoil.  If,  however,  the  aper- 
tures are  constructed  in  such  a  manner  that  the  area  of  aperture 
increases  when  the  velocity  of  the  piston  increases  and  diminishes 
when  that  velocity  diminishes,  the  variation  in  the  area  of  aperture 
may  be  so  regulated  that  the  pressure  in  the  cylinder  will  be  con- 
stant or  will  vary  in  such  a  manner  as  to  keep  the  total  resistance 
to  recoil  constant. 

Both  of  these  methods  have  been  used  in  the  construction  of 
recoil  brakes  for  gun  carriages.  The  brakes  with  constant  orifices 
and  variable  pressures  were  used  on  the  old  carriages  for  15-inch 
smooth  bore  guns. 

For  a  fixed  length  of  recoil  a 'constant  resistance  will  have  a 
lower  maximum  value  than  a  variable  resistance,  and  consequently 
will  produce  a  less  strain  on  the  gun  carriage.  For  this  reason  and 
for  other  advantages  that  will  appear  in  the  discussion  which  fol- 


RECOIL  AND  RECOIL  BRAKES. 


281 


lows,  the  brake  with  variable  orifices,  and  constant  or  variable 
pressure  as  circumstances  may  require,  is  at  present  used  to  the 
exclusion  of  all  others  on  gun  carriages. 

Hydraulic  Brake  with  Variable  Orifice.— The  mode  of  action 
of  the  hydraulic  brake  with  variable  orifices  will  be  understood 


W////7/^  c  m^/m^m^^ 


w//////////////////////^^^ 


FIG.  102. 


FIG.   101. 

from  Fig.  101,  which  represents   a  longitudinal  section  through  a 
recoil  cylinder  of  the  form  used  in  our  seacoast  carriages. 

Fig.   102   represents   a    cross    section    through    the   cylinder. 

To  the  walls  of  the  cylinder  c  are  fastened  two 
bars  o  called  throttling  bars,  of  varying  cross  sec- 
tion as  shown.  The  piston  p  is  stationary,  the 
piston  rod  r  being  fixed  to  a  stationary  part  of  the 
carriage.  The  cylinder  c  is  attached  to  the  gun 
and  moves  to  the  rear  in  recoil. 

The  direction  of  the  movement  of  the  cylinder 
is  to  the  right  in  the  figure.     The  figure  shows  the  relative  positions 
of  cylinder  and  piston  at  the  beginning  of  recoil. 

Through  the  piston  head  are  cut  two  slots  or  apertures,  s, 
through  which  the  liquid  is  forced  from  one  side  of  the  piston  to 
the  other  as  the  cylinder  moves  in  recoil.  Each  slot  has  the  dimen- 
sions of  the  maximum  section  of  the  throttling  bar,  with  just  enough 
clearance  to  permit  operation.  The  area  of  orifice  open  for  the 
flow  of  liquid  at  any  position  of  the  piston  is  therefore  equal  to 
the  area  of  the  slots  minus  the  area  of  cross  section  of  the  throt- 
tling bars  at  that  point;  and  the  profile  of  the  throttling  bars  is 
so  determined  that  the  resistance  to  the  flow  of  the  liquid,  or  the 
pressure  in  the  cylinder,  is  made  constant  or  variable  as  desired. 

165.  Total  Resistance  to  Recoil. — The  total  resistance  to 
recoil  is  composed  of  the  resistance  opposed  by  the  brake,  the  re- 
sistance due  to  friction,  the  resistance — either  plus  or  minus — due 


282  ORDNANCE  AND   GUNNERY. 

to  the  inclination  of  the  top  of  the  chassis,  and  the  resistance  due  to 
the  counter  recoil  springs  if  there  are  such  included  in  the  recoil 
system.  The  function  of  the  counter  recoil  springs  is  to  return  the 
gun  to  battery  after  recoil. 

The  resistance  of  the  counter  recoil  springs  varies  with  the 
degree  of  compression.      Therefore  to  maintain   a   constant  total 
resistance  when  springs  are  included  in  the  system  the  resistance 
of  the  brake  must  also  vary,  the  other  resistances  being  constant. 
Let  W  be  the  weight  of  the  moving  parts, 
M  the  mass  of  the  moving  parts, 
/  the  coefficient  of  friction, 
a  the  angle  of  inclination  of  the  chassis  rails, 
S  the  resistance  of  the  springs  at  any  time  t, 
P  the  total  resistance  of  the  hydraulic  brake,  or  the  total 

pressure  in  the  cylinder,  at  the  time  t, 
R  the  total  resistance  to  motion, 
vr  the  velocity  of  retarded  recoil  at  the  time  t, 
Vr  the  maximum  velocity  of  retarded  recoil. 
The  resistance  due  to  friction  will  be  fWcos  a  ;  that  due  to  the 
inclination  of  the  chassis  rails  will  be  W  sin  a.     The  total  resist- 
ance at  the  time  t  is  therefore 

R  =  W(sina  +  fcosa)  +  S+P  (9) 

Dividing  the  total  resistance  by  the  mass,  we  have,  for  the 
retardation, 

-dv/dt=R/M  (10) 

When  the  total  resistance  to  recoil  is  constant,  the  retardation 
R/M  is  constant,  and  we  may  substitute  it  for  g  in  the  equation 
that  expresses  the  law  of  constant  forces, 


Assuming  the  origin  of  movement  as  at  the  maximum  velocity 
of  recoil,  Vr,  and  designating  by  V  the  length  of  recoil  from  this 
point  to  the  end,  the  above  equation  becomes 

Vr2  =  2l'R/M 
or  l'  =  Vr*M/2R  (11) 


RECOIL  AND   RECOIL  BRAKES.  283 

V  is  the  length  in  which  the  constant  resistance  R  will  overcome  a 
velocity  of  recoil  Vr. 

For  the  velocity  at  any  point  whose  distance  from  the  origin  is 
x,  we  have  the  relation 

(12) 


since  V  —  x  is  the  length  in  which  the  constant  resistance  must  over- 
come the  velocity  vr. 

Values  of  the  Total  and  Partial  Resistances  and  Velocities 
of  Recoil.  —  In  the  construction  of  a  gun  carriage  the  length  of 
recoil  is  usually  fixed  by  the  design  of  the  carriage.  We  will 
therefore  assume  a  length  I  as  the  total  length  of  recoil.  We  must 
now  determine  the  total  constant  resistance  that  will  restrict  the 
recoil  to  this  length  and  then  determine  the  portion  of  this  resist- 
ance that  is  to  be  contributed  by  the  brake.  In  so  doing  we  will 
arrive  at  the  values  of  the  velocities  of  recoil  at  all  points  in  the 
path. 

1  66.  Total  Constant  Resistance.  —  The  curve  vf  in  Fig.  103, 
which  as  far  as  the  point  m  is  the  curve  vf  in  Fig.  100  drawn  to  a 


FIG.  103. 

different  scale,  represents  the  velocity  of  free  recoil  as  a  function 
of  the  time.  We  have  seen  that  the  tangent  to  the  curve  at  any 
point  represents  the  acceleration  at  that  point. 

We  may  represent  the  negative  velocities  due  to  a  constant 
resistance  by  the  ordinates  of  some  straight  line  oc,  whose  ab- 
scissas are  the  corresponding  times.  The  tangent  of  the  constant 


284  ORDXANCE  AND  GUNXERY. 

angle  toe  is  therefore  equal  to  —dv/dt,  the  retardation  due  to  the 
force. 

The  line  oc  is  for  convenience  drawn  above  the  axis  of  t.  As 
its  ordinates  represent  the  negative  velocities  due  to  the  resistance 
the  line  properly  belongs  below  the  axis. 

Now  if  we  subtract  from  the  velocities  of  free  recoil,  repre- 
sented by  the  ordinates  of  the  curve  vf,  the  velocities  due  to  the 
retarding  force,  the  ordinates  of  oc,  the  ordinates  of  the  resulting 
curve  vrt  will  be  the  velocities  of  retarded  recoil.  The  curve  vrt  is 
therefore  the  curve  of  the  velocity  of  retarded  recoil  as  a  function 
of  the  time.  The  abscissas  of  the  curve  being  values  of  t,  the  area 
under  the  curve  will  be  the  total  length  of  retarded  recoil,  see 
equation  (5). 

We  have  assumed  a  total  length  of  recoil,  I,  and  if  the  area 
measured  under  the  curve  of  retarded  recoil,  as  obtained  above, 
does  not  give  this  length,  we  must  change  the  angle  toe,  draw  a  new 
line  oc,  and  construct  a  new  curve.  After  a  few  trials  the  proper 
direction  of  oc  will  be  determined  and  the  area  under  the  curve  of 
retarded  recoil,  vrt  Fig.  103,  will  be  the  length  I. 

Then  the  retardation  represented  by  the  line  oc  is  given,  see 
equation  (10),  by  the  equation 

-  tan  toe  =  -  dv/dt  =  R/M  (13) 

from  which,  after  measuring  the  angle  toe,  we  may  determine  R, 
the  total  constant  resistance  that  will  limit  the  recoil  to  the  length  I. 

The  length  of  retarded  recoil  corresponding  to  any  velocity  of 
retarded  recoil  represented  by  an  ordinate  of  the  curve  rr«  is  the 
area  under  the  curve  from  the  origin  to  the  given  ordinate. 

We  may  nowr  construct  the  curve  of  retarded  recoil  as  a  function 
of  the  distance  recoiled.  To  construct  a  point  of  the  curve  meas- 
ure the  area  under  the  curve  vrt  in  Fig.  103  from  the  origin  to  any 
ordinate;  use  the  value  of  this  area  as  an  abscissa,  and  use  the 
selected  ordinate  of  the  curve  vrt  as  an  ordinate.  The  curve  vrx  in 
Fig.  104,  constructed  in  this  manner  from  the  curve  vrt  in  Fig.  103, 
represents  the  velocity  of  retarded  recoil  as  a  function  of  the  dis- 
tance recoiled. 

Minor  Constant  Resistance. —The  total  resistance  R  is  com- 
posed, equation  (9),  of  the  constant  part  JF(sin  a  +  /cosa)=& 


RECOIL  AND  RECOIL  BRAKES. 


285 


and  the  two  variable  parts  S  and  P.  The  value  of  TF(sin  a  +  /  cos  a) 
may  be  readily  determined.  The  retardation  due  to  this  resistance 
is  equal  to  k/M,  and  is  represented  in  Fig.  103  by  a  line  ok  drawn 
so  that  the  tangent  of  the  angle  tok  is  equal  to  k/M. 


FIG.  104. 

167.  Resistance  of  the  Spring.  —  The  resistance  S  of  a  coiled 
spring  varies  directly  with  the  compression  of  the  spring. 

Representing  by  G  the  force  required  to  compress  the  spring, 
when  free,  over  the  first  unit  of  length,  the  resistance  of  the  spring 
at  any  length  of  compression  x  is 


If  the  spring  has  an  initial  compression  so  that  it  exerts  a 
resistance  G',  the  resistance  after  further  compression  over  a 
length  x  becomes 

(14) 


For  the  counter  recoil  springs  of  a  gun  carriage,  G'  represents 
the  residual  pressure  in  the  spring  when  the  gun  is  in  battery,  and 
x  represents  any  length  of  recoil. 

The  resistance  of  the  spring  at  any  point  may  therefore  be 
determined  from  equation  (14). 

To  find  the  velocities  taken  out  of  the  system  by  the  spring, 
we  proceed  as  follows. 

Representing  by  v'  the  velocity  in  the  mass  M  due  to  the 
spring  alone,  the  retardation  due  to  the  spring  is 


286  ORDNANCE  AND  GUNNERY. 

In  order  to  integrate  we  must  express  dt  in  terms  of  dx. 
dx  =  v'dt.  Therefore 

dt  =  dx/v', 

and  -  dv'/dt  =  -  v'dtf/dx  =  (Gf  +  Gx}/M 

and  integrating, 

-  1/2/2  =  (G'x  +  Gx2/2)/M 

the  constant  of  integration  being  0,  since  when  x  is  0,  v'  is  0. 

The  values  of  vf  are  obtained  from  this  equation  in  terms  of 
x.  We  may  find  from  the  curves  vrx  and  vrt  the  value  of  t  corre- 
sponding to  any  value  of  x.  The  values  of  v'  obtained  above  may 
then  be  laid  off  in  Fig.  103  as  the  true  ordinates  of  the  curve  os. 
These  ordinates  are  laid  off  in  the  figure  from  the  line  ok  so  that  in 
the  figure  the  ordinates  of  os  are  the  sums  of  the  true  ordinates  of 
ok  and  os.  The  ordinates  of  os  are  therefore  the  velocities  taken 
out  of  the  system  by  resistances  other  than  the  hydraulic  brake. 

As  the  ordinates  of  the  line  oc  are  the  velocities  taken  out  by 
the  total  constant  resistance,  the  ordinates  between  the  lines  os 
and  oc  represent  the  velocities  to  be  taken  out  of  the  system  by 
the  brake  alone. 

Resistance  of  the  Hydraulic  Brake,  —  Pressure  in  the  Cyl- 
inder. —  The  pressure  in  the  brake  cylinder  at  any  point  of  the 
recoil  may  now  be  determined  from  equation  (9) 

P=R-W(sina  +  fcosa)-S  (15) 


if  we  substitute  for  R  its  constant  value  from  equation  (13),  for  S 
its  value  at  the  given  point  from  equation  (14),  and  for  the  remain- 
ing term  its  constant  value. 

1  68.  Relation  Between  the  Pressure,  Area  of  Orifice,  and 
Velocity  of  Recoil.  —  In  this  discussion  we  will  designate  by  the 
term  aperture  the  cut  through  the  piston,  and  by  the  term  orifice 
that  portion  of  the  aperture  open  to  the  flow  of  the  liquid;  and  we 
will  consider  for  simplicity  that  there  is  but  one  aperture  and  one 
orifice. 

Let  A  be  the  effective  area  of  the  piston  in  square  feet,  that  is, 
the  area  of  the  piston  minus  the  area  of  the  piston  rod  and  aper- 
ture. The  square  foot  is  taken  as  the  unit  of  area,  because  in  the 


RECOIL  AND  RECOIL  BRAKES.  287 

velocities   involved   in   the  discussion   the   foot   is   the  unit   of 
length. 

Let  a  be  the  area  of  the  orifice  at  any  time  t, 
Vr  the  maximum  velocity  of  retarded  recoil, 
vr  the  velocity  of  retarded  recoil  at  any  time  t, 
vi  the  velocity  of  the  liquid  through  the  orifice  at  the  time  t, 
f  the  weight  of  a  cubic  foot  of  the  liquid, 
P  the  total  pressure  on  the  piston  at  the  time  t. 
The  cylinder  being  full  of  liquid  the  volume  that  passes  through 
the  orifice  is  the  volume  displaced  by  the  piston.     We  therefore 
have  at  any  instant 

vrA  =  vi  a 

or,  tor  the  velocity  of  flow, 

vi  =  VrA/a  (16) 

From  Torricelli's  law  for  the  flow  of  liquids  through  orifices 
we  know  that  the  pressure  required  to  produce  this  velocity  of 
flow  is  the  pressure  due  to  a  column  of  liquid  whose  height  h  is  given 
by  the  equation 

(17) 


Substituting  for  v  the  value  of  vi  from  equation  (16)  and  solving 
for  h  we  obtain 

h  =  v2A2/2ga2  (18)' 

The  weight  of  a  cubic  foot  of  the  liquid  being  7-,  the  weight  of 
the  column  whose  area  of  cross  section  is  unity  will  be  yh,  and  the 
weight  of  the  column  whose  area  of  section  is  equal  to  that  of  the 
piston  will  be  Ayh.  Afh  is  therefore  the  pressure  on  the  piston,  and 
substituting  in  this  expression  the  value  of  h  from  equation  (18)  we 
have,  for  the  total  pressure  on  the  piston,  for  any  velocity  vr 

P=rA3Vr2/2ga2  (19) 

This  equation  is  general  and  expresses  the  relation  that  exists 
between  P,  A,  and  a  for  any  given  velocity  of  recoil. 
Solving  for  a2  we  obtain 

(20) 


288  ORDNANCE  AND  GUNNERY. 

169.  Area  of  Orifice.  —  With  the  relations  established  in  equa- 
tions (14),  (15),  and  (20),  which  are  here  repeated,  and  the  curve 
vrx  in  Fig.  104,  we  are  now  prepared  to  determine  the  variable  area 
of  orifice  in  the  piston. 


(14)  S  = 

(15)  P  =  R-W(sma  +  fcosa)-S 
(20)                      a2  =  rA3vr2/2gP 

The  dimensions  of  the  recoil  cylinder  will  be  fixed  within 
narrow  limits  by  the  design  of  the  carriage,  and  by  the  requirement 
that  the  pressure  per  unit  of  area  must  not  be  so  great  as  to  render 
difficult  the  effective  packing  of  the  stuffing  boxes  through  which 
the  piston  rod  passes.  We  will  therefore  assume  that  the  diam- 
eters of  the  cylinder  and  piston  rod  are  given,  and  as  the  rela- 
tion between  the  total  area  of  piston  and  the  effective  area  may  be 
readily  established  we  will  assume  that  the  effective  area  A  of  the 
piston  is  known. 

Brake  with  Variable  Pressure.  —  The  value  of  P  at  any 
point  in  the  cylinder,  for  which  the  length  of  recoil  is  x,  is  obtained 
from  equation  (15),  the  proper  value  of  S  for  the  point  having  been 
first  determined  from  (14).  The  value  of  vr  is  taken  from  the 
curve  vrx  in  Fig.  104  at  the  ordinate  whose  abscissa  is  x.  The  values 
of  P  and  vr  thus  determined  are  substituted  in  equation  (20). 
The  resulting  value  of  a  is  the  area  of  orifice  at  the  given  point. 

170.  Constant  Pressure.  —  If  P  in  equations  (19)  and  (20)  is 
constant  we  will  have  in  a  given  cylinder,  for  any  other  values  of 
vr  and  a,  as  Vr  and  a0,  respectively  the  maximum  velocity  of  recoil 
and  the  maximum  area  of  orifice 

a02  =  TA3Vr2/2gP  (21) 

and  by  combining  equations  (20)  and  (21)  we  obtain  for  any  given 
cylinder 

a/a0  =  Vr/Vr  (22) 

from  which  we  see  that  to  maintain  a  constant  pressure  in  the 
cylinder  the  area  of  the  orifice  must  vary  directly  with  the  velocity 
of  recoil. 


RECOIL  AND  RECOIL  BRAKES.  289 

Assuming  the  maximum  velocity  of  recoil  as  the  origin  of 
movement  and  substituting  in  equation  (22)  the  value  of  vr/Vr 
obtained  by  combining  equations  (11)  and  (12),  in  which  I'  repre- 
sents the  total  length  of  recoil  after  the  maximum  velocity  has  been 
reached,  we  obtain 

I       x 
a  =  a<Ajl-y  (23) 

that  is,  with  constant  pressure  in  the  cylinder  the  area  of  orifice 
varies  as  the  ordinates  of  a  parabola. 

Equation  (23)  and  all  equations  in  which  V  appears  refer  only 
to  that  part  of  the  recoil  from  the  maximum  velocity  to  the  end  of 
recoil. 

Brake  with  Constant  Pressure. — When  there  are  no  springs 
or  other  variable  resistance  in  the  recoil  system,  8  becomes  0  in 
the  value  of  P,  equation  (15),  and  a  constant  resistance  will  be 
required  in  the  brake. 

To  determine  the  area  of  orifice  we  have,  for  this  case, 

P  =  R—  W(s'm  a  +  f  cos  a) 

(21)  a02  =  M3Fr2A/Pj 

(22)  a/a0  =  vr/Vr 

Find  the  value  of  P  from  the  first  equation  in  the  manner 
already  explained  on  page  286. 

The  maximum  ordinate  of  the  curve  vrx,  Fig.  104,  is  the  value 
of  Vr  in  equation  (21).  A  is  known.  The  maximum  area  of  ori- 
fice a0  may  be  now  determined  from  equation  (21)  and  the  area  of 
orifice  at  all  other  points  more  simply  by  means  of  equation  (22), 
using  the  values  of  vr  taken  from  the  curve  vrx.  The  areas  from  the 
maximum  velocity  to  the  end  may  also  be  obtained  from  equation 
(23). 

Horizontal  Chassis.— If  the  chassis  rails  are  horizontal  and  the 

'top  carriage  is  mounted  on  rollers,  so  that  we  may  neglect  the 

friction,  the  term  W (sina  +  /cosa)  in  the  value  of  P,  equation 

(15),  also  becomes  zero,  and  P  reduces  to  R.    Substituting  for  R 

in  equation  (11)  the  value  of  P  from  (21)  and  solving  for  a0  we 

obtain 

(24) 


290 


ORDNANCE  AND  GUNNERY. 


The  maximum  area  of  orifice  is  in  this  case  independent  of  the 
velocity  of  recoil,  and  is  dependent  only  on  the  length  of  recoil. 
Therefore  for  a  given  maximum  area  of  orifice  the  length  of  recoil 
will  be  the  same  no  matter  what  the  initial  velocity  of  the  projectile, 
the  charge  of  powder,  or  the  angle  of  fire  may  be. 

Under  these  conditions  the  brake  requires  no  adjustment  for 
varying  conditions  of  fire,  and  in  this  respect  it  possesses  further 
advantage  over  the  brake  with  constant  orifices  and  variable 
pressure. 

The  explanation  of  the  independence,  under  the  given  condi- 
tions, of  the  length  of  recoil  and  the  velocity  will  appear  if  we  sub- 
stitute P  for  R  in  equation  (11).  We  obtain 


l'=MVr2/2P 


(25) 


In  equation  (21)  we  see  that  for  a  given  maximum  area  of 
orifice  the  pressure  P  must  vary  directly  as  Vr2  varies.  Therefore 
in  (25),  P  varying  with  Vr2,  I'  will  remain  constant. 

171.  Profile  of  the  Throttling  Bar. — Suppose  there  are  n  similar 
apertures  cut  in  the  piston.  The  area  of  each  orifice  at  any  point 

in  the  cylinder  will  then  be  a/n, 
a  being  determined  for  the  par- 
ticular point  from  equation  (20). 
Let  6,  Fig.  105,  be  the  width  and  d 
the  depth  of  each  aperture.  The 
throttling  bar  has  the  same  depth, 
and  a  variable  width  y. 

Then  for  the  area  of  each  orifice 
at  the  given  point  in  the  cylinder 
we  have 
FIG.  105.  a/n  =  d(b  —  y) 

For  the  brake  with  constant  pressure  the  profile  of  the  throttling 
bar  from  the  point  of  maximum  velocity  to  the  end  will  be  a  par- 
abola. Its  equation,  obtained  by  substituting  the  value  of  a  from 
the  above  equation  in  equation  (23)  and  reducing,  is 


RECOIL  AND  RECOIL  BRAKES.  291 

Neglected  Resistances. — In  the  foregoing  discussion  we  have 
neglected  the  resistance  due  to  the  friction  of  the  liquid  and  the 
contraction  of  the  liquid  vein.  It  has  been  found  by  experiment 
that  the  error  due  to  the  neglect  of  these  resistances  may  be  cor- 
rected by  assigning  to  vi,  the  velocity  of  the  flow  through  the  ori- 
fices, equation  (16),  a  value  greater  than  the  actual  value  as  ex- 
pressed in  equation  (17).  The  value  to  be  substituted  is  deter- 
mined by  experiment  for  each  class  of  carriage  and  takes  the  form 
vs  =  avi  +  b,  a  and  b  being  constants.  The  result  of  the  substitution 
is  an  increase  hi  the  area  of  orifice  for  any  given  pressure  in  the 
cylinder,  see  equation  (20). 

172.  Recoil  System  of  Seacoast  Carriages. — The  arrangement 
of  the  parts  of  the  recoil  system  on  our  seacoast  disappearing  car- 
riages, and  on  barbette  carriages  for  guns  8  inches  or  more  in 
caliber,  is  shown  in  Fig.  106. 

The  two  cylinders  c  are  integral  parts  of  the  top  carriage,  the 
top  carriage,  including  the  cylinders,  forming  a  single  steel  casting 
in  the  sides  of  which  above  the  cylinders  are  trunnion  seats,  for  the 
gun  trunnions  in  a  barbette  carriage,  and  for  the  gun  lever  trun- 
nions in  a  disappearing  carriage. 

The  piston  rods  of  the  recoil  cylinders  are  fixed  to  the  chassis  in 
front  and  supported  in  the  rear.  They  enter  the  cylinders  through 
stuffing  boxes.  On  discharge  of  the  piece  the  top  carriage  and 
recoil  cylinders  move  to  the  rear  with  the  gun,  forcing  the  liquid 
in.  the  cylinders  through  the  orifices  in  the  stationary  pistons. 

The  direction  of  the  movement  of  the  cylinders  is  to  the  right  in 
Fig.  106. 

To  equalize  the  pressure  in  the  two  cylinders  their  interiors  are 
connected  at  the  front  by  the  pipe  a  and  at  the  rear  by  the  two 
pipes  d  and  /.  Each  half  of  the  pipes  d  and  /  has  unobstructed 
communication  with  the  other  half  of  the  same  pipe  through  a 
valve  box  v.  A  cross  pipe  b  connects  the  pipe  a  with  the  valve 
box.  A  path  is  afforded  through  the  pipes  a,  6,  and  d  and  /  for  the 
flow  of  liquid  from  one  side  of  the  piston  to  the  other,  which  path,, 
as  well  as  the  orifices  in  the  pistons,  must  be  considered  in  deter- 
mining the  area  of  orifice. 

The  area  of  orifice,  and  consequently  the  length  of  recoil,  is 
calculated  for  standard  conditions  of  loading.  Any  variation  in 


292 


ORDNANCE  AND  GUNNERY. 


FIG.  106. — Recoil  System,  Seacoast  Carriages. 


RECOIL  AND  RECOIL  BRAKES.  293 

these  conditions  will  vary  the  length  of  recoil,  and  thus,  in  disap- 
pearing carriages,  vary  the  height  of  the  breech  of  the  gun  above 
the  loading  platform.  Standard  conditions  of  loading  do  not 
always  exist,  and  it  is  therefore  desirable  to  have  means  for  varying 
the  resistance  in  the  cylinders  in  order  that  the  prescribed  length 
of  recoil  may  be  obtained  under  any  conditions,  as  for  instance 
when  reduced  charges  are  being  used. 

For  the  purpose  of  varying  the  area  of  orifice,  and  therefore 
the  resistance  in  the  cylinders,  adjustable  valves  called  throttling 
valves  are  provided  at  vi  and  v2.  The  flow  from  the  pipe  6  into  the 
pipe  d  communicating  with  the  body  of  the  cylinder  is  regulated 
by  the  valve  Vi,  and  the  area  open  to  the  flow  is  affected  to  increase 
or  diminish  the  pressure  in  the  cylinder  as  desired.  The  pipe  d 
and  its  valve  v\  are  for  the  control  of  the  recoil. 

To  control  the  counter  recoil  and  to  bring  the  gun  and  top 
carriage  to  rest  without  shock  as  they  come  into  battery  under  the 
action  of  gravity,  the  counter  recoil  buffer  is  provided.  The  rear 
cylinder  head  is  provided  with  a  cylindrical  recess  into  which  the 
enlargement  n  of  the  piston  rod,  just  in  rear  of  the  piston,  enters 
as  the  carriage  approaches  its  position  of  rest  in  battery.  The 
lug  n  is  slightly  conical,  so  that  the  escape  of  the  liquid  from  the 
recess  is  gradually  obstructed.  The  pipe  /  with  its  valve  v2  assists 
in  the  regulation  of  this  part  of  the  counter  recoil. 

The  valves  vi  and  v2  are  moved  to  increase  or  diminish  the  area 
of  orifice  by  means  of  the  handles  seen  in  the  rear  view,  at  the 
right  of  Fig.  106. 

The  cylinders  are  filled,  through  holes  provided  in  the  top, 
with  a  mineral  oil  called  hydroline.  The  freezing  point  of  the  oil 
is  below  0°  F.  Its  specific  gravity  is  about  0.85.  The  oil  may  be 
drawn  off  through  a  hole  e  in  the  valve  box,  ordinarily  stopped 
with  a  screw  plug. 

The  throttling  bars  are  fastened  to  the  cylinders  by  screw  bolts 
through  the  cylinder  walls,  as  shown  in  Fig.  106. 

Modification  of  Recoil  System. — In  the  recoil  system  just 
described  it  will  be  noticed  that,  at  the  beginning  of  recoil,  as  the 
enlargements  n  of  the  piston  rods  emerge  from  the  recesses  in  the 
rear  cylinder  heads  there  is  around  the  enlargements  but  little 
clearance  by  which  the  oil  displaced  by  their  bulk  in  the  cylinders 


294  ORDNANCE  AND   GUNNERY 

proper  may  enter  the  vacated  recesses.  Consequently  if  the 
cylinders  are  full  of  oil  the  liquid  will  be  forced  with  great  velocity 
through  the  clearances,  and  the  pressure  in  the  cylinders  will  be 
correspondingly  high. 

To  prevent  this  high  pressure,  oil  is  withdrawn  from  the  cyl- 
inders in  sufficient  quantity  to  leave  an  air  space  in  the  cylinders 
nearly  equal  to  the  space  occupied  by  the  enlargements  of  the 
piston  rods,  and  on  emerging  from  the  recesses  the  enlargements 
occupy  the  air  space  without  giving  to  the  liquid  an  excessive 
velocity  of  flow. 

The  removal  of  oil  from  the  cylinders  is  objectionable  in  that 
if  the  cylinders  are  not  completely  filled  with  oil  the  uncovered 
parts  of  the  piston  and  of  the  cylinder  walls  are  attacked  by 
rust. 

It  will  be  noticed,  too,  that  any  movement  of  either  of  the 
throttling  valves  that  control  the  recoil  and  counter  recoil  affects 
the  area  of  orifice.  Therefore  the  regulation  of  the  counter  recoil 
affects  also  the  recoil. 

For  these  reasons  it  has  been  found  desirable  to  separate  the 
two  systems  so  as  to  have  independent  control  of  both  recoil  and 
counter  recoil;  and  in  a  6-inch  disappearing  carriage  now  being 
tested  an  additional  recoil  cylinder  is  fixed  in  the  counterweight  of 
the  carriage.  The  control  of  the  recoil  is  effected  wholly  by  this 
large  cylinder,  and  the  counter  recoil  is  controlled  by  smaller  cyl- 
inders whose  pistons  are  acted  on  by  the  top  carriage  in  the  last 
part  of  its  movement  into  battery. 

Other  advantages  of  this  arrangement  will  appear  in  the  de- 
scription of  the  carriage  in  the  next  chapter. 

173.  Wheeled  Carriages,  Recoil.— To  arrive  at  the  effect  of  the 
recoil  on  a  wheeled  carriage  we  must  consider  the  effects  of  all  the 
forces  that  act  upon  the  carriage.  These  forces  include  the  weight 
of  the  system  composed  of  the  carriage  and  gun,  and  the  various 
forces  developed  by  the  transmission  of  the  powder  pressure  to  the 
points  of  support  of  the  carriage. 

In  Fig.  107  is  represented  the  trail  of  a  wheeled  carriage  with 
the  wheel  and  spade.  For  the  purpose  of  discussion  we  will  as- 
sume that  the  carriage  is  a  rigid  body,  that  the  wheels  are  locked, 
and  that  the  pressure  developed  in  the  gun,  or  the  pressure  de- 


RECOIL  AND  RECOIL   BRAKES. 


295 


veloped  in  the  recoil  system  when  the  gun  recoils  on  the  carriage, 
is  transmitted  to  the  carriage  at  the  point  o. 

The  points  of  application  and  the  directions  of  the  forces 
acting  on  the  carriage  and  of  the  reactions  at  the  points  of  support 
are  represented  in  the  figure. 

<£  is  any  angle  of  elevation, 
P  the  transmitted  pressure. 

Let  M  be  the  mass  of  the  system  composed  of  the  gun  and 

carriage, 
W  its  weight, 
F  =  F'  +  F",  the  total  friction  on  the  ground. 


FIG.  107. 


The  center  of  gravity  of  the  system  is  represented  at  c. 

The  forces  acting  on  the  carriage  are  symmetrically  disposed 
with  respect  to  the  axial  plane,  and  therefore  their  resultant  acts 
in  that  plane. 

A  system  of  forces  acting  in  a  plane  is  completely  known  when 
its  components  in  the  direction  of  two  rectangular  axes  in  the 
plane  and  the  moments  about  any  axis  perpendicular  to  the  plane 
are  determined. 

We  will  assume  the  rectangular  axes- as  horizontal  and  vertical, 
the  vertical  axis  through  the  center  of  gravity  and  the  horizontal 
axis  on  the  surface  of  the  ground. 

The  effect  of  the  forces  acting  on  the  carriage  will  be,  under 


296  ORDNANCE  AND  GUNNERY. 

the  most  general  consideration,  a  movement  of  the  carriage  to  the 
rear,  and  at  the  same  time,  since  the  resistance  to  motion  is  great- 
est at  the  point  of  support  of  the  trail,  there  will  occur  a  movement 
of  rotation  of  the  carriage  about  the  point  of  support. 

Applying  to  the  carriage,  in  the  manner  shown  in  Fig.  107,  all 
the  forces  that  act  upon  it,  we  may  consider  the  carriage  as  a  free 
body  and  may  then  determine  the  values  that  the  forces  must  ha,ve 
in  order  to  produce  in  the  free  body  the  actual  movement  of  the 
carriage  hi  recoil. 

The  movement  of  a  free  rigid  body  acted  on  by  forces  may  be 
considered  as  composed  of  a  movement  of  translation  of  the 
center  of  gravity  and  a  movement  of  rotation  of  the  body  about  the 
center  of  gravity.  The  movements  of  translation  and  of  rotation 
may  be  considered  separately. 

We  have  for  the  equations  of  motion  of  the  center  of  gravity 

Pcoscft-F-S      d*x 

~~      -~ 


T-W-Psmt      d?y 


M  dt2 

The  sum  of  the  moments  of  the  applied  forces  with  reference 
to  an  axis  through  the  center  of  gravity  is  the  same  whether  the 
center  of  gravity  is  in  motion  or  at  rest,  and  is  equal  to  the  product 
of  the  acceleration  of  rotation  into  the  moment  of  inertia  of  the 
body  about  the  axis.  Therefore,  representing  with  small  letters 
the  lever  arms  of  the  forces  with  respect  to  an  axis  through  the 
center  of  gravity,  we  have  the  equation 

Pp+Ff+Dd+Ss-Tt      dW 
~~ 


ki  representing  the  principal  radius  of  gyration  of  the  body. 

174.  CONDITION  OF  MOVEMENT.  —  Now  to  introduce  into  the 
three  general  equations  of  motion,  (26),  (27),  and  (28),  the  condi- 
tion that  the  movement  of  the  free  body  shall  be  the  same  as  the 
movement  of  the  carriage  in  recoil,  we  may  write 

y  =  I  sin  6 


RECOIL  AND  RECOIL  BRAKES.  297 

since  this  condition  holds  in  the  actual  movement  of  the  carriage; 
that  is,  as  long  as  the  point  of  the  trail  is  on  the  ground  the  center 
of  gravity  is  at  the  distance  I  sin  6  from  the  ground. 
Differentiating  y  twice  we  obtain 

dy  =  I  cos  Odd 
d2y  =  I  cos  OcPO  -  1  sin  Odd2 
and  dividing  by  dt2 


dff/dt  is  the  angular  velocity  of  the  carriage  about  the  point  of 
the  trail.  Id6/dt  is  therefore  the  linear  velocity  of  the  center  of 
gravity  about  the  same  point.  Representing  this  linear  velocity 
by  v  we  obtain  from  the  above  equation  after  multiplying  the  last 
term  by  l/l 

d?u      d-d  v2 

-J  =  Z_cos0-TSin0  (29) 

This  equation  expresses  that  the  vertical  acceleration  of  the 
center  of  gravity  rotating  about  the  point  of  the  trail  is  equal  to 
the  vertical  component  of  the  linear  acceleration  Id2d/dt2  about 
that  point,  see  Fig.  107,  minus  the  vertical  component  of  the 
acceleration  along  the  radius  I. 

Any  change  in  the  angle  that  the  trail  makes  with  the  ground 
is  accompanied  by  an  equal  change  in  the  angle  of  revolution  of 
the  body  about  the  center  of  gravity,  see  the  two  angles  6  in  Fig. 
107.  Therefore  the  quantities  d26/dt2  in  equations  (29)  and  (28) 
are  the  same. 

Substituting  the  value  of  d2y/dt2  from  equation  (29)  in  equa- 
tion (27)  we  introduce  into  the  general  equations  the  actual  condi- 
tion of  motion.  We  then  have,  for  the  gun  carriage,  the  three 
equations 

--          * 


-  dt2 

D+T-W-Psm<j> 


Pp  +  Ff+Dd+Ss-Tt_dM 
Aflfc2  ~  dt2 


298  ORDNANCE  AND  GUNNERY. 

We  may  determine  any  three  of  the  quantities  in  these  equa- 
tions if  we  establish,  or  assume,  values  for  the  other  quantities; 
and  in  this  way  we  may  determine  the  effects  that  follow  from 
variations  in  the  values  of  any  of  the  quantities  that  enter  the 
equations. 

The  above  equations  are  applicable  only  while  y  =  l$\nd; 
that  is,  as  long  as  the  point  of  the  trail  remains  on  the 
ground. 

As  the  linear  velocity  of  the  center  of  gravity  is  usually  small 
the  value  of  the  term  v2  sin  0/1  in  equation  (31)  is  very  small  and 
is  generally  neglected  in  computations.  In  the  computations  of 
the  stresses  before  movement  begins  v  is  0. 

175.  Application  of  the  Equations. — The  general  equations 
(26),  (27),  and  (28)  are  applicable  in  the  solution  of  all  problems 
that  involve  the  determination  of  the  stresses,  and  of  the  move- 
ment, produced  by  the  application  of  a  force  or  a  system  of  forces 
to  any  body  or  structure. 

The  equations  have  been  deduced  under  the  most  general 
considerations,  and  while  the  number  of  quantities  that  appear  in 
them  is  greatly  in  excess  of  the  number  of  equations,  it  will  be 
found,  in  practical  application  under  given  conditions,  that  equa- 
tions of  relation  between  the  various  quantities  may  be  readily 
established  in  sufficient  number  to  reduce  the  number  of  unknown 
quantities  in  the  equations  to  three,  whose  values  may  then  be 
determined. 

Thus  to  apply  the  general  equations,  under  given  conditions, 
to  any  given  construction,  such  as  the  gun  carriage  represented 
in  Fig.  107. 

The  intensity  and  direction  of  the  applied  force  or  forces  are 
usually  known  or  assumed.  We  will  therefore  assume  that  in 
equations  (26),  (27),  and  (28)  P  and  </>  are  known. 

For  the  gun  carriage,  the  condition  y  =  l$mO  eliminates  the 
quantity  d2y/dt2  and  brings  the  equations  into  the  forms  (30), 
(31),  and  (32).  A  similar  condition  of  restraint  will  ordinarily  be 
found  in  all  constructions  that  are  free  to  move  in  given  directions 
only. 

In  the  modified  equations,  P,  <f>,  W,  and  M  are  known.  All 
dimensional  quantities  su»;h  as  I,  p,  t,  etc.,  are  determined  from 


RECOIL  AND  RECOIL  BRAKES.  299 

the  known  dimensions  of  the  construction.     ki  may  be  determined. 
6  is  known. 

D  and  T  being  parallel  forces  their  intensities  have  a  relation 
to  each  other  dependent  on  the  distances  of  their  points  of  ap- 
plication from  the  directions  of  the  vertical  components  of  the 
applied  forces,  which  relation  may  be  determined  from  the  known 
dimensions  of  the  construction. 

Representing  by  f  the  coefficient  of  friction  we  have 
F=F'  +  F"  =  fD  +  f'T.  This  equation  and  the  established  rela- 
tion between  D  and  T  provide  two  equations  by  means  of  which 
two  of  the  quantities,  D  and  F  for  instance,  may  be  expressed  in 
terms  of  the  third,  T. 

Neglecting  the  term  v2  sin  6/1,  there  are  now  left  unknown  in 
the  original  equations  the  quantities  T,  S,  d2x/dt2,  d20/dt2. 

If  a  value  of  any  one  of  these  quantities  is  established  by  the 
given  conditions  the  values  of  the  others  may  be  determined  from 
the  equations.  For  instance,  the  problem  may  specify  that  the 
pressure  on  the  spade  shall  not  exceed  a  certain  limit.  Then  S 
would  be  known.  Or  it  may  be  specified  that  there  shall  be  no 
horizontal  movement.  This  would  make  d2x/dt2  =  Q.  Or  that 
there  shall  be  no  rotation;  d20/dt2  =  Q. 

Integrating  the  expression  for  the  value  of  d2x/dt2  we  obtain 
dx/dt  =  v,  the  velocity  hi  the  direction  of  x  as  a  function  of  the 
time,  and  integrating  again  we  obtain  x,  the  distance  passed  over, 
also  as  a  function  of  the  time.  Similarly,  if  the  term  d2y/dt2 
remains  among  the  unknown  quantities. 

Integrating  d26/dt2  we  obtain  the  velocity  of  rotation,  and 
integrating  a  second  time  we  obtain  the  angular  displacement, 
both  as  functions  of  the  time. 

The  problem  is  now  completely  solved. 

If  there  is  no  movement  of  the  body  the  problem  is  much 
simplified,  as  under  that  condition  the  terms  involving  the  dif- 
ferentials and  the  velocity  v  become  0. 

The  equations  are  also  applicable  in  determining  the  relations 
that  must  exist,  in  order  that  any  given  condition  may  be  ful- 
filled, between  the  dimensions  and  weight  of  a  construction  and 
the  forces  applied  to  it.  This  will  be  shown  in  the  following 
problem. 


300  ORDNAXCE  AND  GUNNERY. 

176.  Problem.  —  Determine,  for  the  3-inch  field  carriage,  the 
relations  that  must  exist  between  the  constant  resistance  in  the 
recoil  system  and  the  weight  and  dimensions  of  the  carriage  in 
order  that  there  may  not  be  any  movement  of  the  carriage  when 
the  firing  is  at  zero  elevation. 

In  the  three  equations  (30)  to  (32),  <£,  the  angle  of  elevation, 
becomes  0;  and  since  there  is  to  be  no  movement  of  the  carriage 
the  terms  involving  the  accelerations  and  the  linear  velocity 
become  0.  Without  movement  there  will  be  no  friction  and  F 
will  also  be  0. 

The  three  equations  then  reduce  to 


Pp+Dd+Ss-Tt-Q 

-which  express  the  relations  that  must  exist  between  the  resistance 
P  to  recoil,  the  weight,  and  the  dimensions  of  the  carriage  under 
the  condition  of  stability  imposed. 

As  the  center,  of  gravity  of  the  system  moves  to  the  rear  when 
the  gun  recoils  on  the  carriage,  the  most  unfavorable  position  of 
the  center  of  gravity  must  be  used  in  the  equations.  This  will  be 
the  rearmost  position. 

Design  of  a  Field  Carriage  to  Fulfil  the  above  Conditions.— 
Using  the  equations  established  in  the  preceding  problem,  W,  the 
weight  of  the  system  composed  of  the  gun  and  gun  carriage  must 
be  such  that  when  the  weight  of  the  limber  filled  with  ammunition 
is  added,  the  weight  behind  each  horse  of  the  team  shall  not  exceed 
650  pounds.  The  length  of  the  trail  I  will  be  limited  by  considera- 
tions of  draft  and  of  the  turning  angle  of  the  limbered  carriage. 
The  height  of  the  carriage,  /+P(^=o)>  must  be  such  that  the  gun 
may  be  readily  served  and  not  too  easily  overturned.  The  area 
of  the  spade  must  be  such  that  the  pressure  against  it  will  not 
exceed  80  pounds  per  square  inch,  as  it  is  found  that  in  average 
ground  the  spade  will  not  satisfactorily  prevent  movement  of  the 
carriage  when  the  pressure  against  the  spade  exceeds  this  limit. 
Therefore  the  area  of  the  spade  =£/80. 

By  carefully  weighing  these  and  other  considerations,  and 
assuming  successive  values  for  the  various  quantities  in  the  estab- 


RECOIL  AND  RECOIL   BRAKES. 


301 


lished  equations,  satisfactory  dimensions  for  the  carriage  as  a 
whole  are  finally  determined. 

Similar  equations  are  established  for  each  of  the  individual 
parts  of  the  carriage  in  exactly  the  same  manner  as  explained  for 
the  carriage  as  a  whole.  The  stresses  to  which  each  part  is  sub- 
jected and  the  necessary  strength  and  best  form  of  the  part  to 
perform  its  functions  are  thus  determined. 

The  pressure  P  determined  from  the  above  equations  is  the 
greatest  pressure  that  may  be  transmitted  to  the  carriage  under 
the  condition  of  stability  imposed.  The  3-inch  gun  recoils  on  its 
carriage  and  the  recoil  is  controlled  by  a  hydraulic  brake  and 
counter  recoil  springs.  If  we  neglect  the  friction  of  the  moving 
parts,  P  becomes  at  once  the  maximum  constant  resistance  that 
may  be  permitted  in  the  recoil  controlling  system.  It  is  a  value 
of  R  in  equations  (9)  and  (15).  We  will  then  determine,  as  ex- 
plained under  hydraulic  brakes,  the  length  of  the  recoil  when  op- 
posed by  this  resistance,  and  the  length  so  determined  will  be  the 
minimum  length  of  recoil  that  may  be  permitted  on  the  carriage. 

177.  3-inch  Field  Carriage  Recoil  System. — A  longitudinal 
section  through  the  gun  recoil  system  of  the  3-inch  field  carriage 
is  shown  in  Fig.  108,  drawn  to  a  distorted  scale  hi  order  to  show 
the  parts  more  clearly. 


A  cylindrical  cradle  d,  of  cross-section  as  shown  in  Fig.  109,  is 
pintled  by  the  pintle  p  in  a  part  of  the  carriage  called  the  rocker, 
not  shown.  The  grooves  a  of  the  pintle  are  engaged  by  clips 
provided  on  the  rocker.  The  rocker  embraces  the  axle  of  the 
carriage  and  has  a  movement  in  elevation  which  is  transmitted 
to  the  gun  by  the  cradle. 


302 


ORDXANCE  AND  GUXXERY. 


The  gun  is  provided  with  clips  k  which  engage  the  upper 
flanges  of  the  cradle:  and  when  fired,  the  gun  slides  to  the 
rear  on  the  upper  surface  of  the  cradle.  The  lug  I,  Fig. 

108,  is  an  integral  part  of  the  gun. 
The  counter  recoil  buffer  u  is  at- 
tached to  the  lug  by  a  bolt  t,  and  the 
recoil  cylinder  c  is  attached  to  the 
same  bolt  by  means  of  the  screw  v. 
Integral  with  the  walls  of  the  cyl- 
inder are  three  throttling  bars  o. 
The  piston  head  s  is  provided  with 
three  corresponding  apertures,  Fig. 
109. 

The  hollow  piston  rod  r  is  held 
to  the  front  end  of  the  cradle  by  a 
nut  screwed  on  the  forward  end  of 
the  rod.  The  rod  terminates  at  its 
rear  end  in  the  piston  head  s.  The 
outer  shoulder  formed  on  the  front 
head  /  of  the  recoil  cylinder  receives 

the  thrust  of  the  counter  recoil  springs  m  transmitted  through  the 
annular  spring  support  n,  which  also  serves  to  center  the  cylinder 
in  recoil.  The  flat  coiled  springs  m  extend  continuously  from  the 
front  end  to  the  rear  end  of  the  recoil  cylinder. 

The  gun  in  recoiling  draws  with  it,  by  means  of  the  lug  I,  the 
recoil  cylinder  c,  filled  with  oil,  and  the  counter  recoil  buffer  u. 
The  piston,  attached  to  the  cradle,  does  not  move.  When  the 
forward  end  e  of  the  curve  of  the  throttling  bar  reaches  the  piston 
head  s,  the  apertures  in  the  piston  are  completely  closed  against 
the  flow  of  the  liquid,  and  recoil  ceases.  The  counter  recoil  buffer 
u  has  now  been  drawn  all  the  way  out  of  the  piston  rod. 

Under  the  action  of  the  springs  m,  which  have  been  com- 
pressed by  the  recoil,  the  gun  returns  to  battery.  The  first  part 
of  the  counter  recoil,  during  which  the  counter  recoil  buffer  is  out 
of  the  hollow  piston  rod,  is  unobstructed.  When  the  buffer  enters 
the  piston  rod  the  escape  of  oil  from  inside  the  rod  is  permitted  only 
through  the  narrow  clearance  between  the  rod  and  the  buffer. 
The  resistance  thus  offered  gradually  diminishes  the  velocity  of 


FIG.  109. 


RECOIL  AND  RECOIL  BRAKES.  303 

counter  recoil  and  brings  the  gun  to  rest  without  shock  as  it  comes 
into  battery.  The  buffer  is  cylindrical  for  the  greater  part  of  its 
length,  with  a  clearance  in  the  piston  rod  of  0.025  of  an  inch  on  the 
diameter.  The  diameter  of  the  buffer  gradually  enlarges  over  a 
length  of  three  inches  at  the  rear  until  the  clearance  is  but  1/1000 
of  an  inch  on  the  diameter. 

The  pressure  on  the  piston  due  to  the  recoil  is  transmitted 
through  the  cradle  to  the  pintle  p  and  thence  to  the  carriage. 

The  length  of  recoil  is  45  inches. 

Recoil  System  of  Other  Carriages. — The  recoil-controlling  parts 
of  the  carriages  for  siege  guns,  and  of  the  barbette  carriages  for 
seacoast  guns  six  inches  or  less  in  caliber,  embody  the  same  prin- 
ciples as  the  system  described  above. 


CHAPTER  VIII. 
ARTILLERY  OF  THE  UNITED  STATES  LAND  SERVICE. 

178.  Classification. — Service  artillery  may  be  broadly  divided 
into  two  classes :  mobile  artillery  and  artillery  of  position. 

Mobile  artillery  consists  of  the  guns  designed  to  accompany  or 
to  follow  armies  into  the  field,  and  comprises  mountain,  field,  and 
siege  artillery. 

Artillery  of  position  consists  of  the  guns  permanently  mounted 
in  fortifications.  '  As  the  fortifications  of  the  United  States  are  all 
located  on  the  seacoasts,  the  guns  that  form  their  armament  are 
usually  designated  seacoast  guns. 

Mobile  Artillery. — The  mobile  artillery  of  the  United  States  as 
at  present  designed  will  consist  of  the  following  -guns : 

Gun.  Caliber.  Projectile. 

Mountain  gun  2 . 95  inch  18  Ibs. 

Light  field  gun  2 . 38  inch  1\  Ibs. 

Field  gun  3.0    inch  15  Ibs. 

Field  howitzer  3.8    inch  30  Ibs. 

Heavy  field  gun  3 . 8    inch  30  Ibs. 

Heavy  field  howitzer         4 . 7    inch  60  Ibs. 

Siege  gun  4 . 7    inch  60  Ibs. ' 

Siege  howitzer  6.0    inch  120  Ibs. 

The  selection  of  these  calibers  is  based  on  the  following  prin- 
ciples. The  field  gun,  the  principal  artillery  weapon  of  an  army 
in  the  field,  must  have  sufficient  mobility  to  enable  it  to  accom- 
pany the  rapidly  moving  columns  of  the  army.  Long  experience 
indicates  that  to  attain  the  desired  degree  of  mobility  the  weight 
behind  each  horse  of  the  team  should  not  exceed  650  pounds.  A 

204 


ARTILLERY  OF   THE   UNITED  STATES  LAND  SERVICE.     305 

six  horse  team  is  used  with  the  field  gun.  The  total  weight  of  the 
gun,  carriage,  limber,  and  equipment,  with  a  suitable  quantity  of 
ammunition,  is  therefore  limited  to  3900  pounds.  Limited  by  this 
requirement  the  power  of  the  gun  should  be  as  great  as  it  can  be 
made.  The  shrapnel  being  the  most  important  projectile  of  the 
field  gun  the  caliber  of  the  gun  should  be  such  as  to  give  the 
shrapnel  the  greatest  efficiency.  Consideration  of  these  require- 
ments has  led  to  the  adoption  of  the  3-inch  caliber  for  the  field 
gun  of  our  service. 

A  gun  of  greater  power  will,  on  those  occasions  when  it  can  be 
brought  into  action,  be  more  effective  than  the  3-inch  gun.  The 
heavy  3.8-inch  field  gun,  firing  a  30-pound  projectile  and  possessing 
sufficient  mobility  to  enable  it  to  accompany  the  slower  moving 
columns  of  the  army,  is  therefore  provided.  The  weight  behind 
the  six  horse  team  is  limited  to  4800  pounds.  With  this  weight 
the  gun  is  capable  of  rapid  movement  for  short  distances. 

The  caliber  of  the  siege  gun  is  limited  by  the  requirement  that 
the  weight  of  the  gun  shall  not  exceed  the  draft  power  of  an  eight 
horse  team.  The  draft  power  of  this  team,  for  the  siege  gun,  is 
taken  as  8000  pounds. 

Allowing  for  bad  roads  and  rough  usage  and  for  the  occasional 
necessity  of  covering  considerable  distances  at  high  speed,  the 
draft  power  of  a  horse  for  artillery  purposes  is  taken  as  consider- 
ably less  than  the  draft  power  of  the  horse  used  in  ordinary  com- 
merce. 

The  guns  above  named  are  intended  for  the  attack  of  targets 
that  can  be  reached  by  direct  fire,  that  is,  by  fire  at  angles  of 
elevation  not  exceeding  20  degrees.  For  the  attack  of  targets  that 
are  protected  against  direct  fire  and  for  use  in  positions  so  shel- 
tered that  direct  fire  cannot  be  utilized,  curved  fire,  that  is,  fire 
at  elevations  exceeding  20  degrees,  is  necessary.  There  is  there- 
fore provided,  corresponding  to  each  caliber  of  gun,  a  howitzer  of 
an  equal  degree  of  mobility.  The  howitzer  is  a  short  gun  designed 
and  mounted  to  fire  at  comparatively  large  angles  of  elevation. 

In  order  to  reduce  to  the  minimum  the  number  of  calibers  of 
the  mobile  artillery  and  thus  simplify  as  far  as  possible  the  supply 
of  ammunition  in  the  field,  the  calibers  of  the  guns  and  howitzers 
have  been  so  selected  that,  while  both  guns  and  howitzers  fulfil 


306  ORDNANCE  AXD  GUNXERY. 

the  requirements  as  to  weight  and  power  for  each  degree  of  mobil- 
ity, the  caliber  of  each  howitzer  is  the  same  as  that  of  the  gun  of 
the  next  lower  degree  of  mobility.  That  is,  the  howitzer  corre- 
sponding in  mobility  to  one  of  the  guns  is  of  the  same  caliber  as 
the  next  heavier  gun  and  uses  the  same  projectile. 

As  there  may  be  occasions  when  profitable  use  can  be  made 
of  a  gun  throwing  a  lighter  projectile  than  that  of  the  3-inch 
field  gun,  the  light  field  gun,  2.38-inch  caliber,  is  provided.  The 
weight  of  the  projectile  is  1\  pounds,  this  weight  being  considered 
the  lowest  limit  for  an  efficient  shrapnel.  The  2.38-inch  gun  will 
probably  be  used  for  the  movable  defense  of  seacoast  fortifica- 
tions. 

179.  Advantages  of  Recent  Carriages. — The  chief  difference 
between  the  latest  and  earlier  designs  of  carriages  for  mobile 
artillery  lies  in  the  provision  made  in  the  later  carriages  for  recoil 
of  the  gun  on  the  carriage.  By  this  means  a  part  of  the  force 
produced  by  the  discharge  is  absorbed  in  controlling  the  recoil  of 
the  gun  on  the  carriage,  leaving  only  a  part  available  to  produce 
motion  of  the  carriage;  and  by  the  addition  to  the  end  of  the  trail 
of  a  spade  which  is  sunk  in  the  ground  the  carriage  is  enabled  to 
withstand  the  transmitted  force  without  motion  to  the  rear. 
When  the  spade  is  once  fixed  firmly  in  the  earth  further  firing  of 
the  gun  does  not  produce  recoil  of  the  carriage.  Rapidity  of  fire 
is  thereby  greatly  increased,  and  the  soldier  is  relieved  from  the 
fatiguing  labor  of  running  the  carriage  back  into  battery  after 
each  round. 

Rapidity  of  fire  is  also  increased  by  the  use  of  fixed  ammuni- 
tion, and  by  the  provision  for  a  slight  movement  in  azimuth  of  the 
gun  on  the  carriage.  The  movement  in  azimuth  permits  a  change 
in  the  pointing  of  the  gun  of  three  or  four  degrees  to  either  side 
without  disturbing  the  carriage  after  the  spade  is  set  in  the  ground. 

In  addition,  the  gun  sights  on  all  modern  constructions  are 
fixed  to  some  non-recoiling  part  of  the  carriage  so  that  they  are 
not  affected  by  the  recoil.  The  operation  of  sighting  may  there- 
fore go  on  continuously,  independently  of  the  loading  and  firing. 

Our  service  field  and  siege  carriages,  with  the  exception  of  the 
6-inch  siege  howitzer  carriage,  are  so  designed  that  the  wheels  will 
not  be  lifted  from  the  ground  under  firings  at  zero  elevation. 


FIG.  110. — 2.95-inch  Mountain  Gun. 


FIG.  111.— Transport  of  Trail. 


ARTILLERY  OF  THE   UNITED  STATES  LAXD  SERVICE.     307 

The  Mountain  Gun. — For  mountain  service  the  system  com- 
posed of  gun  and  carriage  must  be  capable  of  rapid  dismantling 
into  parts,  no  one  of  which  will  form  too  heavy  a  load  for  a  pack 
mule.  The  weight  of  the  load,  including  the  saddle  and  equip- 
ment of  the  mule,  should  not  exceed  350  pounds.  The  system 
must  be  capable  of  rapid  reassembling  for  action. 

The  mountain  gun  used  in  our  service,  originally  made  by 
Vickers  Sons  and  Maxim  of  England,  has  a  caliber  of  75  milli- 
meters, or  2.95  inches,  and  fires  projectiles  weighing  12 1  and  18 
pounds.  The  caliber  of  this  piece  will  probably  soon  be  changed 
to  3  inches  so  that  it  may  use  the  same  projectile  as  the  3-inch 
field  gun. 

The  gun  is  made  from  a  single  forging,  and  weighs  complete 
with  breech  mechanism  236  pounds.  Fixed  ammunition  is  used 
in  it.  The  breech  mechanism,  Fig.  110,  is  of  the  interrupted 
screw  type.  The  block  has  two  threaded  sectors  separated  by 
flat  surfaces.  It  is  provided  with  percussion  firing  mechanism  so 
arranged  that  the  gun  cannot  be  fired  until  the  breech  block  is 
fully  closed  and  locked.  The  trigger  to  which  the  firing  lanyard 
is  attached  is  seen  to  the  left  in  the  figure  outside  the  breech.  In 
case  of  a  misfire  the  mechanism  may  be  recocked  without  opening 
the  breech. 

1 80.  The  Carriage. — A  low  wheeled  carriage  is  provided  for  the 
mountain  gun.  The  wheels  are  36  inches  in  diameter  and  have 
a  track  of  32  inches.  The  principal  parts  of  the  carriage  are  the 
cradle,  the  trail  and  elevating  gear,  the  wheels  and  axle. 

THE  CRADLE. — The  cradle  is  a  bronze  casting,  with  a  central 
cylindrical  bore  and  a  smaller  cylinder  on  each  side.  The  central 
cylinder  embraces  the  gun  to  within  a  few  inches  of  the  muzzle 
and  forms  a  support  in  which  the  gun  slides  in  recoil.  The  side 
cylinders  are  hydraulic  buffers  the  piston  rods  of  which  are  secured 
to  lugs  on  the  gun  by  interrupted  screws  so  that  the  gun  may  be 
readily  separated  from  the  cradle.  Grooves  of  varying  width  and 
.depth  cut  in  the  interior  walls  of  the  buffer  cylinders  allow  passage 
of  oil  from  one  side  of  the  piston  to  the  other  in  recoil.  Constant 
pressure  is  maintained  in  the  cylinder  throughout  the  length  of 
recoil,  14  inches.  Spiral  springs  surrounding  the  piston  rods 
return  the  gun  to  battery. 


308  ORDNANCE  AND  GUNNERY. 

The  cradle  is  secured  to  the  trail  by  a  bolt,  seen  above  the 
axle  in  Fig.  110,  which  passes  through  two  lugs  formed  on  the 
under  side  of  the  cradle,  the  outer  ends  of  the  bolt  fitting  into 
two  bearings  or  sockets  provided  at  the  forward  upper  end  of  the 
trail.  The  cradle  moves  in  elevation  about  this  bolt. 

Light  lifting  bars  are  provided  for  use  in   dismantling  and 

assembling  the  gun  and  carriage.     They  are  passed  through  the 

two  eye  bolts  on  the  top  of  the  cradle,  and  through  one  on  the  gun. 

Front  and  rear  sights  are  attached  to  the  cradle.     The  rear 

tangent  sight  is  detachable. 

THE  TRAIL. — The  trail  consists  of  two  outside  plates  or  flasks 
of  steel  joined  together  by  a  shoe  and  three  transoms.  The  shoe 
is  provided  with  a  spade  on  the  under  side  to  assist  in  checking 
recoil,  and  with  a  socket  on  the  upper  side,  in  which  a  handspike 
may  be  fitted,  or  the  shafts  attached  when  traveling  on  wheels. 
At  the  front  end  of  the  trail  are  the  bearings  for  the  cradle  bolt 

and  further  to  the  rear  are  bearings  for 
the  axle.  The  bearings  are  open  at  the 
top,  Fig.  112,  the  openings  having  a 
width  less  than  the  diameter  of  the 
bearing.  The  cradle  bolt  and  axle  tree 
are  cylindrical,  with  flats  cut  on  them 
so  that  they  can  only  enter  their  bear- 
ings at  a  certain  angle.  When  in  position  in  the  bearings  they  are 
turned  through  90  degrees  and  thus  secured.  The  crank  secured 
to  the  axle  at  the  right,  Fig.  110,  is  for  the  purpose  of  turning  the 
axle,  in  dismantling  the  carriage,  to  bring  the  flats  of  the  axle  in 
line  with  the  openings  of  the  bearings.  When  assembled  the  axle 
is  locked  in  position  by  a  spring  latch  bolt  in  the  crank  handle 
which  engages  in  a  slot  provided  in  the  trail. 

THE  ELEVATING  GEAR. — The  elevating  gear  is  permanently 
attached  to  the  trail.  Motion  of  the  hand  wheel,  Fig.  110,  is  com- 
municated to  the  gun  through  bevel  gears,  6  Fig.  113,  a  worm, 
w,  and  a  toothed  quadrant,  q,  attached  at  its  rear  end  to  the 
cradle.  An  arm  formed  on  the  forward  end  of  the  quadrant  em- 
braces the  cradle  bolt  and  revolves  around  it.  A  cross  bar,  c, 
on  each  side  near  the  upper  end  of  the  arm  keeps  the  quadrant  in 
a  central  position,  and  two  spiral  springs  fastened  to  the  front 


CRADLE 


FIG.  113. 


ARTILLERY  OF  THE   UNITED  STATES  LAND  SERVICE.     309 

transom  and  acting  on  the  arm  maintain  practically  a  uniform 
weight  on  the  elevating  gear  while  the  gun  is  being  elevated 
or  depressed. 

The  gun  may  move  in  eleva- 
tion from  minus  10  degrees  to 
plus  27  degrees. 

1 8 1 .  Ammunition.  —  Fixed 
ammunition  is  used.  The  charge 
is  about  8  ounces  of  smokeless 
powder.  The  110-grain  percussion 
primer  is  used  in  the  cartridge 
case  and  a  front  igniter  of  about 
|  ounce  of  black  rifle  powder. 
Three  kinds  of  projectiles  are  pro- 
vided: canister,  shrapnel,  and 
high  explosive  shell.  The  canis- 
ter and  shrapnel  weigh  12|  Ibs.,  the  high  explosive  shell  18  Ibs. 
The  canister  contains  244  cast  iron  balls  each  f  of  an  inch  in 
diameter.  The  shrapnel  contains  234  balls.  The  bursting  charge 
for  the  shell  is  2.07  Ibs.  of  high  explosive. 

The  muzzle  velocity  of  the  12^-lb.  projectile  is  850  feet.  The 
maximum  pressure  in  the  bore  is  18,000  Ibs. 

The  gun  has  an  effective  range  of  about  4000  yards. 

Transportation. — For  purposes  of  transportation  the  gun  and 
carriage,  with  tools,  implements,  and  equipments,  are  divided  into 
four  loads,  the  principal  items  of  which  are  the  gun,  the  cradle, 
the  trail,  the  wheels  and  axle.  These  loads,  without  the  pack 
equipment,  weigh  approximately  250  Ibs.  each.  The  pack  saddle 
and  equipment  weigh  90  Ibs.,  so  that  the  total  weight  carried  by 
the  mule  is  about  340  Ibs. 

The  trail,  which  forms  the  most  inconvenient  load,  is  shown 
in  Fig.  Ill,  loaded  on  the  pack  animal. 

The  ammunition  is  carried  in  nine  loads  of  10  or  12  rounds 
each,  according  as  the  projectiles  weigh  18  or  12|  Ibs.  A  box 
holding  5  or  6  rounds  is  slung  on  hooks  on  each  side  of  the  pack 
saddle  by  loops  formed  in  wire  straps  about  the  box.  The  boxes 
open  at  the  end  so  that  the  ammunition  may  be  removed  from 
them  without  disturbing  the  pack. 


310 


ORDNANCE  AND   GUNNERY. 


Field  Artillery. — The  field  artillery  as  at  present  designed  will 
consist  of  the  2.38-inch  gun,  the  3-inch  gun,  the  3.8-inch  gun, 
and  the  3.8-inch  and  4.7-inch  howitzers.  It  is  also  the  intention  to 
modify  the  carriage  of  the  mountain  gun  so  that  the  piece  may 
be  fired  at  high  angles  of  elevation  and  be  used  as  a  light  field 
howitzer.  The  caliber  of  the  gun  will  then  be  changed  to  3  inches 
so  that  the  projectiles  of  the  3-inch  field  gun  may  be  used  in  it. 
There  is  also  at  present  in  service  a  3.6-inch  field  mortar. 

Fixed  ammunition  is  used  in  all  field  pieces  except  the  mortar. 

The  following  table  contains  data  relating  to  the  guns  and 
carriages  of  the  field  artillery, 


Guns. 

Howitzers. 

Mortar. 

Caliber,  inches  

2.38 
1905 

3 
1905 

3.8 
1905 

3.8 
1906 

4.7 
1906 

3.6 

1890 

Date  of  Model  

Charge,  Ibs     .    .           .        ... 

0.72 
7.5 
0.8 
9.5 
118 
1700 
3.3000 
2400 

15 
19.4 
664 
5800 

1.62 
15 
0.82 
18.75 
252 
1700 
33000 
3900 

15 
21.9 
737 
6100 

3 
30 
2.1 
38 
526 
1700 
33000 
4800 

15 
21 
769 
6900 

1.2 

30 
2.1 
35 
526 
900 
15000 
3900 

45 
36.3 
707 
6300 

1.3 
60 
3.1 
65 
1063 
900 
15000 
4800 

45 
37.4 
752 
6850 

0.38 
20 
0.6 

690 
17000 

45 
21.2 
515 
3360 

Projectile,  Ibs.  .  .        

Uursting  charge,  Ibs  

Cartridge  complete,  Ibs  

Shrapnel  balls,  number  

Muzzle  velocity,  f.  s  

Maximum  pressure,  Ibs  

Weight,  limbered,  Ibs  

AT    MAXIMUM    ELEVATION. 

Elevation,  degrees  

Time  of  flight,  seconds  

Remaining  velocity,  f.  s  

Range,  yards  

Other  data  concerning  the  guns  of  the  field  artillery  will  be 
found  in  the  table  on  page  135. 

The  velocities  and  pressures  are  fixed  at  the  low  figures  given 
in  the  table  in  order  that  the  guns  and  carriages  may  be  kept  within 
the  limits  as  to  weight. 

With  velocities  of  400  feet  the  service  shrapnel  balls  are  effec- 
tive against  men,  and  with  velocities  of  880  feet,  against  animals. 
As  the  velocity  of  the  balls  is  increased  by  from  250  to  300  feet  at 
the  bursting  of  the  shrapnel,  it  will  be  seen  from  the  table  that 
shrapnel  fire  from  the  field  pieces  is  effective  at  all  ranges. 

The  designs  of  the  field  guns  of  different  caliber,  with  their 
mounts,  differ  practically  only  in  the  size  of  the  parts.  A  de- 
scription of  one  will  therefore  answer  for  all. 


ARTILLERY  OF  THE  UNITED  STATES  LAND  SERVICE.     311 

182.  The  3-inch  Field  Gun. — The  3-inch  field  gun  is  the  prin- 
cipal weapon  of  the  field  artillery.  The  gun,  of  nickel  steel,  is 
built  up  in  the  manner  described  on  page  236.  A  hoop  called  the 
clip  is  shrunk  on  near  the  muzzle.  On  the  under  side  of  this  hoop, 
and  of  the  locking  hoop  and  jacket,  are  formed  clips,  k  Fig.  117, 
which  embrace  the  guide  rails  of  the  cradle  of  the  carriage.  The 
gun  slides  in  recoil  on  the  upper  surface  of  the  cradle.  A  down- 
wardly extending  lug,  I  Figs.  116  and  117,  at  the  rear  of  the  jacket 
serves  for  the  attachment  of  the  recoil  cylinder,  which  moves  with 
the  gun  in  recoil. 

THE  BREECH  MECHANISM. — The  breech  mechanism,  model 
1904,  is  shown  in  Fig.  114,  in  the  locked  position.  The  mechan- 
ism is  of  the  slotted  screw  type. 


FIG.  114. 


The  breech  block  6  is  cylindrical  with  four  threaded  and  four 
slotted  sectors.  It  is  mounted  on  a  hollow  spindle  s  formed  on 
the  carrier  c,  to  which  it  is  held  by  the  lug  n,  which  engages  in  a 
slot  cut  in  the  enlarged  base  of  the  spindle.  On  a  semi-circular 
boss  formed  on  the  rear  face  of  the  block  is  cut  a  toothed  rack, 


312 


ORDNANCE  AND  GUNNERY. 


outlined  at  z,  Fig.  117.  The  teeth  of  a  bevel  pinion  formed  on  the 
inner  end  of  the  operating  lever  g  mesh  in  the  teeth  of  the  rack. 
The  lever  is  pivoted  on  a  pin  which  passes  through  two  lugs  formed 
on  the  rear  face  of  the  carrier.  On  grasping  the  handle  of  the 
lever  the  pressure  against  a  latch  t  in  the  handle  unlocks  the  lever 
from  the  face  of  the  breech.  Swinging  the  lever  to  the  rear  ro- 
tates the  block  until  it  is  stopped  by  a  lug  inside  the  carrier  and 
locked  in  position  by  the  spring  stud  a.  Further  movement  of  the 
lever  causes  both  block  and  carrier  to  rotate  together  about  the 
hinge  pin  h.  When  the  movement  is  nearly  complete  the  surface 
o  of  the  carrier  bears  against  the  arm  of  the  extractor  lever  y, 
which  causes  the  extractor  x  to  move  sharply  to  the  rear  and 
eject  the  empty  cartridge  case. 

183.  THE   FIRING   MECHANISM. — The   firing  mechanism,   Fig. 
115,  is  contained  in  the  firing  lock  case  /,  which  is  inserted  into  the 


b 


FIG.  115. 


hollow  spindle  from  the  rear,  the  interrupted  lugs  d  on  the  lock 
case  engaging  behind  corresponding  interrupted  lugs  c  on  the 
carrier.  Assembled  in  the  lock  case  are  the  firing  pin  p,  the  spiral 
firing  spring,  the  firing  pin  sleeve  w,  and  the  trigger  fork  v,  the 
latter  fitting  over  the  squared  end  of  the  trigger  shaft  h,  which  is 
journaled  in  an  arm  of  the  lock  case  /,  Fig.  117,  extending  down- 
ward and  to  the  right  outside  the  carrier. 

At  the  lower  end  of  the  trigger  shaft  h,  Fig.  117,  are  two  levers 
at  right  angles  to  each  other,  one  marked  trigger  provided  with 


ARTILLERY  OF   THE   UNITED  STATES  LAXD  SERVICE.       313 

an  eye  for  the  hook  of  the  lanyard,  the  other  acted  upon  by  an 
upwardly  extending  lug  on  the  end  of  the  firing  lever  shaft. 

A  narrow  section  of  the  forward  end  of  the  lock  case,  Fig.  115, 
is  cut  out  for  the  flat  sear  spring  r.  A  notch  in  the  sear  engages 
the  shoulder  formed  on  the  firing  pin.  The  sleeve  w  at  its  rear 
end  bears  upon  the  last  coil  of  the  firing  pin  spring.  When  the 
trigger  shaft  h  is  turned  by  a  pull  on  the  lanyard,  or  by  means  of 
the  firing  lever,  the  trigger  fork  v  forces  the  sleeve  w  to  the  front, 
compressing  the  firing  spring.  The  forward  end  of  the  sleeve 
pushes  the  sear  spring  aside  from  its  engagement  on  shoulder  of 
firing  pin,  and  the  compressed  spring  then  drives  the  firing  pin 
forcibly  forward  until  arrested  by  the  shoulder  striking  the  inner 
surface  of  the  spindle.  When  the  pull  on  the  lanyard  has  ceased, 
the  firing  spring,  still  compressed,  exerts  a  pressure  against  the 
rear  end  of  the  sleeve  w,  thence  on  the  fork  v,  and  on  the  head  o  of 
the  firing  pin;  and  the  construction  of  these  parts  is  such  that 
the  spring  can  regain  its  extended  length  only  when  the  parts  are  in 
the  position  shown  in  the  figure.  The  firing  pin  is  therefore  im- 
mediately withdrawn,  on  the  cessation  of  the  lanyard  pull,  until 
caught  again  by  the  sear. 

The  system  of  cocking  and  firing  the  piece  by  one  movement 
is  called  the  continuous  pull  system.  The  firing  spring  is  com- 
pressed only  at  the  moment  of  firing,  whereas  in  the  mechanism 
that  is  cocked  in  opening  the  breech  the  firing  spring  is  com- 
pressed whenever  the  breech  is  opened  and  may  remain  com- 
pressed for  a  long  time. 

SAFETY  DEVICES. — Safety  against  discharge  before  the  breech 
is  fully  closed  is  secured  as  follows.  The  axis  of  the  spindle  s 
on  the  carrier,  Fig.  114,  lies  TV  of  an  inch  below  and  ^  of  an  inch 
to  the  right  of  the  axis  of  the  gun.  The  breech  block  which  re- 
volves oh  this  spindle  is  therefore  eccentric  with  the  bore.  The 
firing  mechanism  is  eccentric  with  the  block,  the  axis  of  the  firing 
mechanism  being  fixed  in  the  axis  of  the  bore.  When  the  block 
is  locked  the  hole  in  its  front  end  through  which  the  firing  pin 
protrudes  in  firing  is  also  in  the  axis  of  the  bore,  but  as  the  block 
is  rotated  in  opening,  the  hole  rotates  out  of  the  axis  of  the  bore 
and  the  flat  surface  at  its  rear  end  comes  in  front  of  the  firing  pin 
and  prevents  movement  of  the  firing  pin  until  the  breech  is  locked. 


314  ORDNANCE  AND  GUNNERY. 

The  headed  spring  pin  u,  Fig.  117,  enters  a  hole  in  the  carrier 
and  retains  the  firing  mechanism  in  its  position  in  the  carrier. 
By  withdrawing  this  pin  and  rotating  the  firing  lock  case  /  upward 
through  45  degrees  the  interrupted  lugs  d,  Fig.  115,  on  the  firing 
lock  case  disengage  from  behind  the  interrupted  lugs  c  on  the 
carrier,  and  the  firing  mechanism  may  be  withdrawn  from  the  gun. 
The  breech  block  is  then  readily  removed.  The  breech  mechan- 
ism may  thus,  without  the  use  of  tools,  be  readily  dismantled  for 
repair,  or  the  gun  may  be  quickly  disabled  in  the  event  of  imminent 
capture. 

Four  holes  are  drilled  rearwardly  through  the  breech  block,  b 
Fig.  114,  to  permit  the  escape  of  gas  without  injury  to  the  screw 
threads  of  the  mechanism  in  case  the  primer  in  the  cartridge  is 
punctured  by  the  blow  of  the  firing  pin. 

THE  3-iNCH  GUN,  MODEL  1905.— The  3-inch  gun,  model  1905, 
is  50  Ibs.  lighter  than  the  1902  and  1904  models,  the  outside  diam- 
eters being  slightly  diminished.  The  twist  of  the  rifling,  which 
in  the  earlier  models  increases  from  1  turn  in  50  calibers  at  the 
breech  to  1  in  25  at  the  muzzle,  increases  from  zero  at  the  breech 
to  1  in  25  at  9J  inches  from  the  muzzle,  from  which  point  it  is 
uniform  to  the  muzzle.  The  purpose  of  the  change  in  twist  is 
to  dimmish  the  resistance  encountered  by  the  projectile  hi  the 
first  part  of  its  movement  and  thereby  diminish  the  maximum 
pressure.  The  short  length  of  uniform  twist  at  the  muzzle  steadies 
the  projectile  as  it  issues  from  the  bore. 

184.  The  Carriage. — The  principal  parts  of  the  carriage  are  the 
cradle,  the  rocker,  the  trail,  the  wheels  and  axle. 

THE  CRADLE. — The  cradle,  c  Figs.  116  and  117,  is  a  long  steel 
cylinder,  which  contains  the  recoil  controlling  parts.  These  parts 
are  fully  described  in  the  chapter  on  recoil,  and  illustrated  in 
Figs.  108  and  109  of  that  chapter.  The  gun  slides  in  recoil  on  the 
upper  surface  of  the  cradle,  the  clips  of  the  gun,  k  Fig.  117,  en- 
gaging the  flanged  edges.  A  pintle  plate  fastened  to  the  bottom 
of  the  cradle  is  provided  with  the  pintle  p,  Fig.  117,  and  the 
grooved  arc  a,  which  serve  to  connect  the  cradle  to  the  rocker. 

THE  ROCKER. — The  rocker  r  embraces  the  axle  between  the 
flasks  of  the  trail  by  the  bearings  at  its  ends.  The  cradle  pintle 
fits  in  a  seat  provided  in  the  rocker  above  the  axle,  and  the  clips 


ARTILLERY  OF  THE   UNITED  STATES  LAND  SERVICE.     315 


FIG.  116. 


FIG.  117. 


316  ORDNANCE  AND  GUNNERY. 

on  the  rocker  engage  in  the  grooved  arc  a  of  the  cradle.  This  con- 
struction permits  movement  of  the  cradle  and  gun  in  azimuth  on 
the  rocker,  while  the  rocker  itself  revolves  about  the  axle  and  thus 
gives  movement  in  elevation  to  the  cradle  and  the  gun.  The 
movement  in  azimuth,  4  degrees  either  way,  is  produced  by  a 
screw  on  the  shaft  of  the  hand  wheel  t,  Fig.  116.  The  shaft  is 
fixed  in  bearings  in  the  rocker  arms  and  the  screw  works  in  a  nut 
pivoted  in  a  bracket  fastened  under  the  cradle. 

The  double  elevating  screw,  actuated  by  either  of  the  crank 
shafts  e  fixed  in  bearings  in  the  trail,  rotates  the  rocker  and  cradle 
about  the  axle.  The  bevel  pinion  on  the  end  of  each  shaft  e  rotates 
the  bevel  pinion.  6  in  its  bearings.  The  pinion  b  is  splined  to  the  outer 
screw  m  and  causes  the  outer  screw  to  turn  in  the  fixed  nut  q  which 
is  supported  below  the  pinion  6  by  a  transom.  The  outer  screw  m 
has  a  left  handed  thread  on  the  exterior  and  a  right  handed  thread 
in  the  interior.  When  turned  it  travels  up  or  down  hi  the  nut  q, 
and  at  the  same  time  causes  the  inner  screw  n  to  move  into  or  out 
of  the  outer  screw,  the  inner  screw  being  prevented  from  turning 
by  its  connection  with  the  rocker,  arms,  r  Fig.  116.  The  move- 
ment of  the  inner  screw  for  each  turn  of  the  pinion  6  is  thus  equal 
to  the  sum  of  the  pitches  of  the  outer  and  inner  screws. 

THE  TRAIL. — The  trail,  Fig.  119,  composed  of  two  flanged  steel 
flasks  connected  by  transoms  and  top  and  bottom  plates,  ter- 
minates at  its  lower  end  in  a  fixed  spade  provided  writh  a  float  or 
wings  which  prevent  excessive  burying  of  the  spade  in  the  ground. 
The  lower  edge  of  the  spade  is  of  hardened  steel  riveted  on  so  that 
it  may  be  readily  replaced  when  worn  out.  The  lunette,  a  stout 
eye  bolt  fixed  in  the  end  of  the  trail,  engages  over  the  pintle  of  the 
limber  when  the  carriages  are  connected  for  traveling.  Seats  for 
two  cannoneers  who  serve  the  piece  in  action  are  attached  to  the 
trail  one  on  either  side  near  the  breech  of  the  piece;  and  two  other 
seats  on  the  axle,  facing  toward  the  muzzle,  are  occupied  in  trav- 
eling by  two  cannoneers,  one  of  whom  manipulates  the  lever  of 
the  wheel  brakes. 

THE  WHEELS  A.ND  AXLE. — The  axle  of  forged  steel  is  hollow. 
The  axle  arms  are  given  a  set  so  as  to  bring  the  lowest  spoke  of 
each  wheel  vertical. 

The  wheels  are  a  modified  form  of  the  Archibald  pattern,  56 


ARTILLERY  OF   THE   UNITED  STATES  LAND  SERVICE.    317 


FIG.  118. 
The  hollow  axle  forms  a  reservoir  for 


inches  in  diameter  with  3-inch  tires.     The  hub,  Fig.  118,  consists 

of  a  steel  hub  box  h  and  hub  ring  r 

assembled    by    bolts    through    the 

flanges,  between  which   the  spokes 

of  the  wheel  are  tightly  clamped. 

The  hub  box  is  lined  with  a  bronze 

liner  forced  in.    A  steel  cap  c  is 

screwed  on  the  outer  end  of    the 

hub  box.     Riveted  to  the  cap  is  a 

self  closing  oil  valve,  by  means  of 

which  the  wheels  are  oiled  without 

removal  from  the  axle. 

the  oil. 

The  wheels  are  secured  to  the  axle  by  the  wheel  fastening,  a 
bronze  split  ring,  hinged  for  assembling  around  the  axle.  The 
ring  revolves  freely  in  a  groove  in  the  axle.  Interrupted  lugs  on 
its  exterior  engage  behind  corresponding  interrupted  lugs,  /  Fig. 
118,  in  the  inner  end  of  hub  box,  and  hold  the  wheel  on  the  axle. 
A  hasp  connects  the  hub  and  the  wheel  fastening  so  that  they 
cannot  revolve  independently  and  disengage  the  lugs. 

185.  THE  SHIELD. — The  cannoneers  serving  the  piece  are  pro- 
tected by  a  shield  of  hardened  steel  r2¥  of  an  inch  thick.  It  is  in 
three  parts.  One  part,  the  apron,  depends  from  the  axle  and  is 
swung  up  forward  under  the  cannoneers'  seats  when  traveling. 
The  main  shield,  rigidly  attached  to  the  frame  of  the  carriage, 
extends  upwards  from  the  axle  to  2J  inches  below  the  tops  of  the 
wheels.  The  top  shield  is  hinged  to  the  main  shield.  When 
raised  its  upper  edge  is  62  inches  from  the  ground,  a  height  suffi- 
cient to  afford  protection  from  long  range  and  high  angle  fire  to 
cannoneers  on  the  trail  seats.  In  traveling  the  top  shield  is  folded 
over  so  that  should  the  carriage  turn  over  on  the  march  the  shield 
is  partially  protected  from  injury.  Each  shield  before  being  at- 
tached to  the  carriage  is  tested  at  a  range  of  100  yards  with  a 
bullet  from  the  service  rifle.  The  plate  must  not  be  perforated, 
cracked,  broken,  or  materially  deformed  in  the  test. 

SIGHTS. — The  piece  is  provided  with  three  different  means  of 
sighting.  Two  fixed  sights  on  the  upper  element  of  the  gun, 
Figvl!6,  determine  a  line  of  sight  parallel  to  the  axis,  for  use  in 


318  ORDNANCE  AND  GUNNERY. 

giving  general  direction  to  the  piece.  For  more  accurate  sighting 
a  tangent  rear  sight  and  a  front  sight  with  crossed  wires  are  pro- 
vided. They  are  seated  in  brackets  attached  to  the  cradle.  A 
telescopic  panoramic  sight  is  seated  on  the  stem  of  the  tangent 
sight.  This  sight  is  used  for  direct  aiming  and  for  indirect  aiming, 
which  consists  in  pointing  the  gun  by  means  of  a  line  of  sight  con- 
siderably divergent  from  the  line  of  fire.  By  means  of  the  pano- 
ramic sight  any  object  in  view  from  the  gun  may  be  used  as  an 
aiming  point. 

A  range  quadrant,  seated  on  the  cradle  of  the  carriage,  pro- 
vides the  means  of  determining  the  elevation  in  indirect  fire. 

The  sights  are  fully  described  in  the  chapter  on  sights,  Chapter 
XIII,  and  the  range  quadrant  in  Chapter  XIV. 

The  Limber. — The  limber,  Fig.  120,  is  practically  wholly  of 
metal,  the  neck  yoke  and  pole,  and  spokes  and  felloes  of  the 
wheels,  being  the  only  wooden  parts.  The  body  of  the  limber  is  a 
steel  frame,  composed  of  three  rails  riveted  to  lugs  formed  on  the 
axle  and  braced  by  steel  tie  rods.  The  middle  rail  is  in  the  form 
of  a  split  cylinder,  one  half  passing  below  the  axle  and  the  other 
above.  The  halves  unite  in  front  forming  a  socket  for  the  pole, 
which  is  held  firmly  in  place  by  a  clamp.  Similarly  in  the  rear  the 
middle  rail  forms  a  seat  for  the  pintle  hook.  The  pintle  hook  is 
swiveled  in  its  seat,  so  that  if  at  any  time  the  gun  carriage  turns 
over  the  pintle  will  turn  without  overturning  the  limber  as 
well. 

The  ammunition  chest,  of  sheet  steel,  is  fastened  to  the  outer 
rails.  The  front  of  the  chest  and  the  door  which  forms  the  rear 
are  strengthened  by  vertical  corrugations.  The  door  opens  down- 
ward and  is  then  supported  by  chains.  The  metallic  ammunition 
is  supported  in  the  chest  by  three  diaphragms  each  perforated 
with  39  holes.  The  middle  and  rear  diaphragms  are  connected  by 
flanged  brass  tubes  cut  away  on  top  to  reduce  the  weight.  The 
tubes  support  the  front  ends  of  the  cartridge  cases  and  enable 
blank  ammunition  and  empty  cases  to  be  carried. 

Seats  made  of  sheet  steel  are  provided  for  three  cannoneers  on 
the  limber  chest,  and  a  steel  foot-plate  rests  on  the  rails  in  front 
of  the  chest. 

The  wheels  of  the  limber  and  the  wheels  of  all  other  carriages 


Fi-3.   119.— 3-inch  Field  Gun,  Model  1902. 


FIG.  120.— 3-inch  Field  Limber. 


Fig.   121. — 3-inch  Field  Gun,   Limbered. 


FIG.  122.— 3-inch  Field  Caisson. 


FIG.   123. — 3-inch  Field  Battery  Wagon. 


FIG.  124.— 3-inch  Field  Store  Wagon. 


ARTILLERY  OF   THE   UNITED  STATES  LA.\D  SERVICE.     319 

that  form  part  of  a  field  battery  are  interchangeable  with  the 
wheels  of  the  gun  carriage. 

186.  The  Caisson  and  other  Wagons.— The  construction  of 
the  caisson,  Fig.  122,  does  not  differ  materially  from  that  of  the 
limber.  The  ammunition  chest  is  larger  and  carries  70  rounds  of 
ammunition.  The  front  of  the  chest  is  of  armor  plate  •&  of  an 
inch  thick;  and  the  door  at  the  rear,  which  opens  upward  to  an 
angle  of  about  30  degrees  above  the  horizontal,  is  of  armor  plate 
Ty^  of  an  inch  thick.  A  TVinch  plate  also  depends  from  the  axle 
as  in  the  gun  carriage.  The  cannoneers  serving  the  caisson  are 
thus  afforded  protection  for  a  height  of  63  inches  from  the  ground. 

Attached  to  the  caisson  by  a  hinged  bracket  at  the  rear  is  an 
automatic  fuse  setter,  by  means  of  which  the  cannoneer  at  the 
caisson  may  quickly  set  the  fuse  of  the  projectile  to  the  time  of 
burning  corresponding  to  any  range  ordered  by  the  battery  com- 
mander. The  fuse  setter  is  described  in  the  chapter  on  primers 
and  fuses,  and  is  illustrated  in  Fig.  229. 

Three  caissons  with  their  limbers  accompany  each  gun  into 
the  field. 

The  wagons  of  a  batteiy  include  also  the  forge  limber,  which, 
as  its  name  indicates,  carries  a  blacksmith's  forge  and  set  of  tools; 
and  the  battery  wagon,  Fig.  123,  which  carries  carpenter's  and 
saddler's  tools  and  supplies;  materials  for  cleaning  and  preserva- 
tion; spare  parts  of  gun,  of  carriage,  and  of  harness;  tools  and 
implements;  miscellaneous  supplies  and  two  spare  wheels. 

A  wagon  called  the  store  wagon,  Fig.  124,  is  for  use  in  carrying 
such  stores,  spare  parts,  and  materials  as  cannot  be  carried  hi  the 
battery  wagon. 

Experiments  are  now  being  conducted  toward  the  develop- 
ment of  an  automobile  battery  wagon. 

Field  Howitzers  and  Mortars. — The  3.8-inch  and  4.7-inch 
field  howitzers  have  not  yet  been  constructed.  The  principles  of 
construction  of  the  guns  and  carriages  will  be  understood  from  the 
description  of  the  6-inch  howitzer  and  carriage  which  follows  later. 

There  is  at  present  in  service  a  3.6-inch  field  mortar  shown  in 
Fig.  125.  The  piece  is  a  short  gun  intended  for  vertical  fire  against 
troops  protected  by  intrenchments  or  other  shelter.  The  Freyre 
obturator  described  on  page  262  is  used  in  the  breech  mechanism 


320 


ORDNANCE  AND   GUNNERY. 


to  save  weight.  The  gun  weighs  245  Ibs.  and  its  mount  300  Ibs. 
more,  so  that  the  gun  with  its  mount  may  be  readily  moved  in  the 
field.  The  mount  is  a  single  steel  casting.  The  gun  is  held  at  any 
desired  elevation  by  means  of  a  clamp  which  acts  on  a  steel  arc 
attached  to  the  under  side  of  the  gun. 

When  in  use  the  carriage  rests  on  a  wooden  platform,  and 
recoil  is  checked  by  a  heavy  rope  attached  to  stakes  driven  into 
the  ground  in  front. 


187.  Siege  Artillery. — The  new  siege  artillery  comprises  the 
4.7-inch  gun  and  the  6-inch  howitzer.  The  older  siege  pieces  now 
in  service  are  the  5-inch  gun,  the  7-inch  howitzer,  and  the  7-inch 
mortar. 

The  following  table  contains  data  relating  to  the  guns  and 
carriages  of  the  siege  artillery. 


Guns. 

Howitzers. 

Mortar. 

Caliber,  inches  

4.7 
1904 

5 
1898 

6 

1905 

7 
1898 

7 
1892 

Date  of  model  

Charge,  Ibs  

5.94 
60 
3.1 
73J 
1063 
1700 
33000 
8000 

15 
21.8 
971 
7600 

5.37 
45 
1.75 

1830 
35000 

8800 

31" 
38.2 
638 
10000 

4 
120 
3.  86 

2150 
900 
15000 
7COO 

45 
37.5 
764 

7000 

4.6 
105 
7.4 

1100 
-SOOO 

35 
34.3 
749 
7700 

4.0 
125 
11.9 

800 

1:0000 

45 
32.9 
641 
5200 

Projectile,  Ibs  

Bursting  charge,  Ibs  

Cartridge  complete,  Ibs  

Shrapnel  balls,  number  

Muzzle  velocity,  f.  s  

Maximum  pressure,  Ibs  

Weight,  limbered,  Ibs  

AT  MAXIMUM   ELEVATION. 

Elevation,  degrees  

Time  of  flight,  seconds  

Remaining  velocity,  f.  s  

Range,  yards  

ARTILLERY  OF   THE   UNITED  STATES  LAND  SERVICE.     321 

Other  data  concerning  the  guns  of  the  siege  artillery  will  be 
found  in  the  table  on  page  135. 

The  4.7-inch  Siege  Gun. — The  gun  is  similar  in  construction 
and  in  breech  mechanism  to  the  3-inch  field  gun.  Fixed  ammu- 
nition is  used  in  it. 

THE  CARRIAGE. — The  carriage  is,  in  general,  similar  in  con- 
struction to  the  3-inch  field  carriage.  The  greater  weight  of  the 
gun  and  the  increased  force  of  recoil  render  necessary  certain 
changes  in  the  parts.  In  the  3-inch  carriage  the  recoil  cylinder 
and  counter  recoil  springs  are  assembled  together  in  a  single  cyl- 
inder in  the  cradle.  The  cradle  of  the  4.7-inch  carriage,  Figs.  127, 
128,  and  129,  consists  of  three  steel  cylinders  bound  together  by 
broad  steel  bands,  the  middle  band  provided  with  trunnions. 
The  middle  cylinder  contains  the  mechanism  for  the  hydraulic 
control  of  recoil.  Each  of  the  outer  cylinders  contain  three  con- 
centric columns  of  coiled  springs  for  returning  the  gun  to  battery. 
The  front  end  of  each  of  the  outer  two  spring  columns  is  connected 
to  the  rear  end  of  the  next  inner  column  by  a  steel  tube,  flanged 
outwardly  at  the  front  end  and  inwardly  at  the  rear  end.  A 
headed  rod  passes  through  the  center  of  the  inner  coil  and  is  fixed 
to  a  yoke  that  is  fastened  to  the  lug  at  the  breech  of  the  gun,  see 
Fig.  128.  The  head  of  the  rod  acts  on  the  inner  coil  only,  and  the 
pressure  is  transmitted  through  the  flanged  tubes  or  stirrups  to 
the  outer  coils.  In  this  way  the 
springs  work  in  tandem  and  have  a 
long  stroke  with  short  assembled 


length. 


©oooooo 
The  arrangement  of   the  springs 

luooooooooof] 

"  "   . :-— ~-    ^  -  '  j 


ooooooooo 


ooooooooo 


r 

3--. 


& 


OOOOOOOO: 


oooooooo: 


will  be  understood  by  reference  to 
Fig.  126,  in  which  r  represents  the 
headed  rod,  s  the  tubular  stirrups,  and 
c  the  walls  of  the  cradle  cylinder.  FIG.  126. 

The  length  of  recoil  is  66  inches. 

The  gun  is  supported,  and  slides  in  recoil,  on  rails  r  fixed  on 
top  of  the  spring  cylinders.  The  distance  apart  of  the  rails  broad- 
ens the  bearing  of  the  gun  and  gives  it  steadiness  both  in  action 
and  in  transportation.  An  extension  piece,  bolted  to  the  front 
end  of  the  cradle  and  readily  detachable,  continues  the  rails  to 


322 


ORDNANCE  AND  GUNNERY. 


the  front  clip  of  the  gun.     When  traveling  this  extension  piece 
is  detached  and  carried  in  fastenings  under  the  trail. 

THE  PINTLE  YOKE. — The  cradle  is  trunnioned  in  a  part  called 
the  pintle  yoke,  y  Fig.  127,  which  is  itself  pintled  in  a  seat,  p, 
called  the  pintle  bearing,  mounted  between  the  forward  ends  of 
the  trail  flasks,  its  rear  end  embracing  the  hollow  axle  x.  A 
traversing  bracket,  6,  is  attached  to  the  bottom  of  the  pintle  yoke 
and  extending  to  the  rear  under  the  axle  forms  a  support  for  the 


FIG.  127. 


traversing  shaft  t  and  for  the  elevating  mechanism.  The  rear  end 
of  the  traversing  bracket  slides  on  supporting  transoms  between 
the  flasks  of  the  trail,  motion  being  given  to  the  bracket  by  means 
of  a  screw  on  the  traversing  shaft  which  works  in  a  nut  suitably 
attached  to  the  trail.  The  gun  may  be  moved  in  azimuth  on  the 
carriage  4  degrees  either  way.  The  elevating  mechanism  is  car- 
ried on  the  traversing  bracket  and  moves  with  the  gun  in  azi- 
muth. It  is  therefore  not  subjected  to  any  cross  strains.  The 
gun  may  be  moved  in  elevation  from  minus  5  to  plus  15  degrees. 

1 88.  THE  WHEELS  AXD  THE  TRAIL. — The  wheels  are  60  inches 
in  diameter  with  5-inch  tires.     Exhaustive  tests  recently  con- 


ARTILLERY  OF   THE    UNITED  STATES  LAND  SERVICE.     323 

eluded  indicate  that  no  practical  advantage  is  gained  by  the  use 
of  wider  tires  on  vehicles  of  this  class  and  weight. 

The  trail  is  of  the  usual  construction,  two  pressed  steel  flasks 
of  channel  section  tied  together  by  transoms  and  plates.  The 
front  ends  of  the  flasks  are  riveted  to  cast  steel  axle  bearings 
which  extend  to  the  front  of  the  axle  and  support  between  them 
the  pintle  bearing  p.  The  location  of  the  pintle  socket  in  front 
of  the  axle  permits  the  use  of  a  shorter  trail  and  reduces  the  weight 
at  end  of  trail  to  be  lifted  in  limbering. 

Bearings  are  provided  at  about  the  middle  of  the  trail,  in  the 
opening  seen  in  Fig.  128,  for  a  detachable  geared  drum  which  is 
used  in  giving  initial  compression  to  the  counter  recoil  springs  in 
assembling,  and  in  withdrawing  the  gun  to  its  traveling  position. 
When  not  in  use  the  drum  is  kept  in  the  tool-box  in  the  trail. 

The  spade  with  its  horizontal  floats  is  hinged  to  the  trail  on 
top.  For  traveling  it  is  turned  up  and  rests  on  top  of  the  trail, 
see  Fig.  129;  for  firing  it  is  turned  down.  In  either  position  it  is 
locked  in  place  by  a  heavy  key  bolt. 

A  bored  lunette  plate  is  riveted  to  the  bottom  of  the  trail,  for 
engagement  on  the  pintle  of  the  limber. 

The  Limber. — The  limber,  Fig.  130,  is  merely  a  wheeled  turn- 


FIG.  130. 


table  for  the  support  of  the  end  of  the  trail  in  traveling.  It  has 
the  usual  arrangements  for  the  attachment  of  the  team.  Its 
wheels  are  interchangeable  with  those  of  the  carriage.  The 
turntable,  shaped  to  fit  the  end  of  the  trail,  is  mounted  on  a  frame 


324  ORDXAXCE  AND   GUNXERY. 

fixed  to  the  axle.     It  forms  a  seat  for  the  trail.     The  seat  is 
pivoted  at  the  rear  end  and  its  front  end  rests  on  rollers  which 
travel  on  a  circular  path  on  the  limber.     A  pintle  on  the  seat  en- 
gages in  the  lunette  in  the  bottom  of  the  trail. 

When  traveling,  in  order  to  distribute  the  weight  as  evenly  as 
possible  between  the  front  and  rear  wheels  of  the  limbered  carriage, 
the  gun  is  disconnected  from  the  piston  rod  and  spring  rods,  and 
drawn  back  40  inches  to  the  rear,  Fig.  129.  In  this  position  the 
recoil  lug  is  secured  between  two  stout  braces  attached  to  a  heavy 
trail  transom.  The  breech  of  the  gun  is  thus  supported  and 
rigidly  held  in  traveling,  and  the  elevating  and  traversing  mech- 
anisms are  relieved  from  all  strains.  The  braces  referred  to  are 
pivoted  in  the  trail,  and  when  not  in  use  are  turned  down  inside 
the  trail. 

189.  Weights. — The  weight  of  the  gun  carriage  complete  is 
4440  Ibs.,  and  that  of  the  gun  and  carriage,  7170  Ibs.  The  weight 
at  the  end  of  the  trail,  gun  in  firing  position,  or  the  weight  to  be 
lifted  in  limbering,  is  400  Ibs.;  with  the  gun  in  traveling  position, 
this  is  increased  to  1150  Ibs.,  which  is  the  part  of  the  weight  of 
the  gun  carriage  sustained  by  the  limber. 

Siege  Limber  Caisson. — For  the  transportation  of  ammuni- 
tion for  siege  batteries  there  is  provided  a  vehicle  called  the  siege 
limber  caisson.  As  the  name  indicates,  this  vehicle  is  composed  of 
two  parts.  Each  part  supports  an  ammunition  chest  arranged  to 
carry  28  rounds  of  4.7-inch  ammunition  or  18  rounds  of  6-inch 
ammunition,  thus  making  56  rounds  of  4.7-inch  ammunition  or 
36  rounds  of  6-inch  ammunition  per  vehicle.  For  each  siege 
battery  of  4  guns  16  limber  caissons  are  provided. 

The  6-inch  Siege  Howitzer. — This  is  a  short  piece,  13  calibers 
long,  mounted  on  a  wheeled  carriage  so  constructed  that  the 
piece  can  be  fired  at  angles  of  elevation  from  minus  5  to  plus  45 
degrees.  This  wide  range  of  elevation  on  a  wheeled  mount  in- 
troduces into  the  carriage  requirements  not  encountered  in  the 
construction  of  the  carriages  previously  described,  which  provide 
for  a  maximum  elevation  of  15  degrees. 

The  piece  is  made  from  a  single  forging,  Fig.  131.  A  lug,  /, 
extends  upward  from  its  breech  end  for  the  attachment  of  the 
recoil  piston  rod  and  the  yoke  for  the  rods  of  the  spring  cylinders. 


ARTILLERY  OF   THE  UNITED  STATES  LAND  SERVICE.     325 

Flanged  rails  r  formed  above  the  piece  support  it  on  the  cradle  of 
the  carriage,  on  which  the  piece  slides  in  recoil. 

The  operating  lever  of  the  breech  mechanism  of  the  gun,  Figs. 
132  and  133,  is  above  the  axis  of  the  gun  instead  of  below  it  as 
in  other  guns.  It  is  so  placed  for  the  purpose  of  increasing  the 
clearance  in  recoil  and  for  convenience  in  operating. 


FIG.  .131. 

190.  The  Carriage.— The  cradle,  Figs.  132  and  133,  is  pro- 
vided with  recoil  and  spring  cylinders.  The  arrangement  of  the 
springs  in  the  spring  cylinders  is  the  same  as  shown  in  Fig.  126 
for  the  4.7-inch  siege  gun.  The  gun  is  placed  below  the  cylinders 
in  order  that  the  center  of  gravity  of  the  system  may  be  as  low  as 
possible.  The  trunnions  of  the  cradle  rest  in  beds  in  the  top 
carriage,  which  in  turn  rests  on  and  is  pintled  in  the  part  called 
the  pintle  bearing.  Flanges  on  the  top  carriage  engage  under 
clips  on  the  pintle  bearing.  The  forward  ends  of  the  trail  flasks 
are  riveted  to  the  pintle  bearing,  which  forms  a  turntable  on  which 
the  top  carriage,  and  the  parts  supported  by  it,  have  a  movement 
of  three  degrees  in  azimuth  to  either  side.  The  traversing  is  ac- 
complished by  means  of  the  hand-wheel  t  on  the  left  side.  The 
traversing  shaft  is  supported  in  a  bracket,  a,  fixed  to  the  left  flask, 
and  its  worm  works  in  a  nut,  o,  pivoted  to  the  top  carriage. 

THE  ROCKER. — The  rear  part  of  the  rocker  is  a  U-shaped  piece 
that  passes  under  the  gun  and  is  attached  to  the  cradle  by  the  hook 
k,  pivoted  in  the  cradle.  Arms  extend  forward  from  the  sides  of 
the  U  and  embrace  the  cradle  trunnions  between  the  cradle  and 
the  cheeks  of  the  top  carriage,  so  that  the  rocker  may  rotate 
about  the  cradle  trunnions.  The  sights  are  seated  on  a  bar  sup- 
ported on  the  left  vertical  arm  of  the  rocker.  The  upper  end  of 
the  elevating  screw  n  is  attached  to  the  bottom  of  the  rocker, 
while  the  lower  end  of  the  screw  and  the  elevating  gear  are  sup- 


326 


ORDNANCE  AND  GUNNERY. 


ARTILLERY  OF  THE   UNITED  STATES  LAND  SERVICE.     327 

ported  by  trunnions  in  lugs  on  the  under  side  of  the  top  car- 
riage. The  rocker  therefore  moves  in  elevation  in  the  top  carriage 
and  gives  elevation  to  the  gun-supporting  cradle  fastened  to  the 
rocker  by  the  hook  k.  The  elevating  apparatus  is  operated  by  a 
hand-wheel  e  on  either  side. 

THE  TRAIL. — The  flasks  of  the  trail  extend  separately  to  the 
rear  a  sufficient  distance  to  permit  free  movement  between  them 


FIG.  133. 

of  the  gun  in  recoil  at  any  elevation.  They  are  then  joined  by 
transoms  and  top  and  bottom  plates,  and  terminate  in  a  detachable 
spade  which  is  secured  to  the  top  of  the  trail  when  traveling. 
Sockets  are  provided  for  two  handspikes  at  the  end  of  the  trail. 
Two  lifting  bars  are  also  fixed  to  the  trail.  In  order  to  permit  the 


328  ORDNANCE  AND  GUNNERY. 

desired  movement  of  the  cradle  in  elevation  the  axle  is  in  three 
parts,  the  middle  part  lower  than  the  two  axle  arms.  The  three 
parts  are  held  by  shrinkage  in  cylinders  formed  in  the  sides  of  the 
pintle  bearing. 

The  wheel  brakes,  used  both  hi  firing  and  hi  traveling,  are 
manipulated  by  hand-wheels  b  in  front  of  the  axle. 

191.  RECOIL  CONTROLLING  SYSTEM. — The  feature  of  this  car- 
riage which  chiefly  differentiates  it  from  other  carriages  described 
is  the  provision  for  the  automatic  shortening  of  recoil  as  the  ele- 
vation of  the  gun  is  increased.  From  minus  5  degrees  to  0  eleva- 
tion the  gun  has  a  recoil  of  50  inches.  As  the  elevation  increases 
from  0  to  25  degrees  the  length  of  recoil  diminishes  continuously 
from  50  inches  to  28  inches.  For  elevations  between  25  and  45 
degrees  the  length  of  recoil  rmeains  at  28  inches.  The  variation 
in  length  of  recoil  is  necessitated  by  the  approach  of  the  breech  to 
the  transoms  and  to  the  ground  as  the  piece  is  elevated. 

The  automatic  regulation  of  recoil  is  produced  in  the  following 
manner.  Four  apertures  are  cut  in  the  piston  of  the  recoil  cyl- 
inder and  two  longitudinal  throttling  grooves  in  the  walls  of  the 
cylinder.  The  total  area  of  apertures  and  deepest  section  of  the 
grooves  is  the  proper  maximum  area  of  orifice  for  the  50-inch 
length  of  recoil,  while  the  grooves  alone  furnish  the  proper  con- 
tinuous area  of  orifice  for  a  recoil  of  28  inches.  A  disk  rotatably 
mounted  on  the  piston  rod  against  the  front  of  the  piston,  and 
provided  with  apertures  similar  to  those  in  the  piston  and  similarly 
placed,  is  rotated  on  the  piston  rod  during  the  recoil  of  the  piece 
by  two  lugs  projecting  into  helical  guide  slots  cut  in  the  walls  of 
the  recoil  cylinder.  The  rotating  disk  gradually  closes  the  aper- 
tures in  the  piston,  and  the  twist  of  the  guiding  slots  is  such  that 
the  area  of  orifice  is  varied  as  required  for  limiting  to  50  inches  the 
recoil  of  the  gun  when  fired  at  0  elevation. 

The  recoil  cylinder  is  rotatably  mounted  in  the  cradle.  Teeth 
cut  on  its  outer  surface,  Fig.  134,  mesh  in  the  teeth  of  a  ring  sur- 
rounding the  right  spring  cylinder,  and  the  teeth  of  the  ring  also 
mesh,  at  any  elevation  between  0  and  25  degrees,  in  a  spiral 
gear  cut  on  the  cylindrical  block  s,  which  is  seated  in  the 
hollow  trunnion  of  the  cradle  and  is  fast  to  the  right  cheek 
of  the  top  carriage.  As  the  gun  is  elevated  from  0  to  25 


ARTILLERY  OF  THE   UNITED  STATES  LAND  SERVICE.     329 


degrees  the  spiral  teeth  of  the  gear  cause  the  ring  to  rotate 

clockwise  and  the  cylinder  counter 

clockwise.      The    rotating    recoil 

cylinder  carries -with  it  the  disk 

in  front  of  the  piston,  causing  the 

disk  to  close  the  piston  apertures 

more  and  more  until  at  25  degrees 

elevation     they    are     completely 

closed.       The   throttling   grooves 

in    the    walls    of     the     cylinder 

then    provide    the    proper    area 

of  orifice  for  the  28-inch  length  FIG.  134. 

of  recoil  permitted  to  the  gun  at  elevations  between  25  and  45 

degrees. 

LOADING  POSITION. — To  load  the  piece  after  firing  at  high  an- 
gles the  hook  k,  which  holds  the  cradle  to  the  rocker,  is  disengaged 
by  means  of  a  handle,  h,  conveniently  placed  on  top  of  the  cradle, 
and  the  cradle  and  gun  are  swung  by  hand  to  a  convenient  position 
for  loading.  The  center  of  gravity  of  the  tipping  parts  is  in  the  axis 
of  the  trunnions.  A  pawl,  3,  attached  to  the  cradle  automatically 
engages  teeth,  4,  on  the  top  carriage  and  retains  the  gun  in  the 
loading  position  until  released  by  means  of  the  same  handle  h 
that  was  used  to  disengage  the  cradle  hook. 

As  the  sights  and  elevating  screw  are  attached  to  the  rocker, 
their  positions  are  not  affected  by  the  position  of  the  piece  in  load- 
ing. The  operations  of  laying  the  piece  may  therefore  be  per- 
formed at  the  same  time  as  the  loading. 

STABILITY  OF  THE  CARRIAGE. — The  piece  is  set  low  in  the  car- 
riage to  diminish  as  far  as  possible  the  overturning  moment;  but 
the  maximum  velocity  of  free  recoil  of  this  light  piece  is  so  great 
that  stability  of  the  carriage  at  all  angles  of  elevation  could  not 
be  obtained  without  exceeding  the  limit  of  weight  and  making  the 
recoil  unduly  long.  The  carriage  will  be  stable  for  angles  of  eleva- 
tion greater  than  about  10  degrees.  The  wheels  are  expected  to 
rise  from  the  ground  in  firings  at  angles  of  elevation  less  than  10 
degrees. 

THE  LIMBER. — The  limber  is  the  same  as  the  limber  of  the 
4.7-inch  siege  carriage  previously  described.  When  limbered  the 


330 


ORDNANCE  AND  GUNNERY. 


rear  end  of  the  cradle  is  locked  to  the  trail  in  order  to  relieve  the 
elevating  and  traversing  mechanisms  from  strain.  The  short 
length  of  the  howitzer  renders  it  inadvisable  to  move  the  gun  to  a 
more  rearward  traveling  position. 

WEIGHTS. — The  weight   of  gun  and  carriage  is  about   6900 
pounds,  and  the  weight  of  the  limber  1000  pounds.    The  total 


PIG.  136. 


weight  is  slightly  less  than  the  limit  of  8000  pounds,  considered  as 
a  maximum  load  for  a  siege  team. 

192.  Siege  Artillery  in  Present  Service. — The  wheeled  siege 
pieces  in  present  service  are  the  5-inch  gun,  shown  in  Fig.  135, 
and  the  7-inch  howitzer,  Fig.  136. 


ARTILLERY  OF  THE   UNITED  STATES  LAND  SERVICE.     331 

When  emplaced  in  a  siege  battery  the  carriage  for  either  piece 
rests  on  a  wooden  platform.  Recoil  is  limited  by  means  of  a 
hydraulic  buffer  attached  to  the  trail  and  pintled  in  front  to  a 
heavy  pintle  fixed  to  the  platform.  The  howitzer  also  recoils  on 
the  carriage,  the  recoil  of  the  piece  being  controlled  by  hydraulic 
buffers  one  on  each  side  in  front  of  the  trunnions.  Springs,  strung 
on  rods  in  rear  of  the  trunnions,  return  the  gun  to  the  firing  posi- 
tion. The  springs  are  either  coiled  or  Belleville  springs,  the  latter 
being  saucer  shaped  disks  of  steel  strung  face  to  face  and  back  to 
back. 

The  pieces  are  mounted  at  a  height  of  about  six  feet  above  the 
ground  to  enable  the  guns  to  be  fired  over  a  parapet  of  sufficient 
height  to  shelter  the  gunners. 

For  traveling,  the  guns  are  shifted  to  the  rear  into  trunnion 
beds  provided  in  the  trail. 

The  7-inch  siege  mortar  and  carriage  are  shown  in  Fig.  137. 


FIG.  137. 

The  carriage  rests  on  three  traverse  circle  segments  /  bolted  to 
the  platform.  It  is  held  to  the  paltform  by  the  overhanging 
flanges  of  the  segments  g.  Elevation  is  given  to  the  gun  by  means 
of  the  handspike  I  which,  for  the  purpose,  is  seated  in  a  slot  in  the 
trunnion;  and  direction  is  given  by  means  of  the  handspikes  j 
which  are  engaged  against  lugs  on  the  carriage.  The  means  of 


332  ORDNANCE  AND  GUNNERY. 

controlling  the  recoil  of  the  piece  are  similar  to  those  employed 
with  the  7-inch  howitzer. 

193.  Seacoast  Artillery. — Comprised  in  the  seacoast  artillery 
are  guns  ranging  in  caliber  from  2.24  inches  to  16  inches,  their 
projectiles  ranging  in  weight  from  6  pounds  to  2400.  The  2.24-inch 
and  3-inch  guns,  called  the  6-pounder  and  the  15-pounder,  are  used 
for  the  defense  of  the  sea  fronts  of  fortifications  against  landing 
parties  and  for  the  defense  of  the  submarine  mine  fields.  The 
guns  of  medium  caliber,  from  4  to  6  inches,  are  best  used  for  the 
protection  of  places  subject  to  naval  raids,  and  for  the  defense  of 
mine  fields  at  distant  ranges.  Their  fire  is  effective  against  un- 
armored  or  thinly  armored  ships. 

The  8-  and  10-inch  guns  are  effective  against  armored  cruisers 
and  against  the  thinly  armored  parts  of  battleships. 

The  proper  target  for  guns  12  inches  or  more  in  caliber  is  the 
heavy  water  line  armor  of  the  enemy's  battleship. 

The  12-inch  gun  is  the  largest  gun  at  present  mounted  in  our 
fortifications.  One  16-inch  gun  has  been  manufactured  and  satis- 
factorily tested,  but  no  guns  of  this  caliber  are  mounted.  The 
latest  model  of  12-inch  gun  was  designed  to  give  the  1000  pound 
projectile  a  muzzle  velocity  of  2550  feet,  which  would  insure  per- 
foration, at  a  range  of  8700  yards,  of  the  12-inch  armor  carried  by 
the  latest  type  of  battleship.  But  it  has  been  found  that  in  the 
production  of  this  high  muzzle  velocity  in  a  heavy  projectile  the 
erosion  due  to  the  heat  and  great  volume  of  the  powder  gases  is 
so  great  as  to  materially  shorten  the  life  of  the  gun.  It  has  been 
decided  therefore  as  a  measure  of  economy  to  reduce  the  muzzle 
velocities  of  the  larger  guns  from  2550  feet  to  2250,  and  to  build 
for  the  defense  of  such  wide  waterways  as  cannot  be  properly 
defended  by  the  12-inch  guns  with  the  reduced  velocity,  14-inch 
guns  which  will  give  to  a  1660-pound  projectile  a  muzzle  velocity 
of  2150  feet,  sufficient  to  insure  perforation  of  12-inch  armor  at  a 
range  of  8700  yards. 

The  wide  channels  that  exist  at  the  entrances  to  Long  Island 
Sound,  Chesapeake  Bay,  Puget  Sound,  and  Manila  Bay  will  require 
these  14-inch  guns  for  their  defense. 

The  table  following  contains  data  relating  to  seacoast 
guns. 


ARTILLERY   OF   THE   UNITED  STATES   LAND  SERVICE.     333 


BO 

£ 

For  Maximum  Range. 

.D 

5 

IH 

£ 

Gun. 

Date  of 

1 

JS 

tj 

if 

q 

c  — 

Model. 

aT 
1 

1 

•3  c 

4)  O 

c   / 

«  bi 

3j"  •/ 

«•§ 

"c~ 

'Sc 

If" 

• 

a 

f 

3 

3** 

C""1 

S.-C 

s  ^ 

E*   OS 

£^*"" 

o 

£ 

n 

S 

a 

S 

w 

H 

ft 

2.24-inch 

19JO 

1.35 

6 

0.25 

2400 

34000 

18 

7600 

25.1 

695 

3-inch 

1903 

6.06 

15 

0.35 

3000 

340(10 

15 

8500 

24.1 

776 

4.72-  inch 

Armstrong 

10.5 

45 

1.96 

2600 

340:10 

15 

IOC  00 

26.4 

718 

5-inch 

1900 

26 

58 

2.75 

3000 

36000 

15 

10900 

27.0 

865 

6-inch 

1905 

42 

106 

4.6 

2900 

36000 

15 

12400 

29.4 

926 

8-inch 

1888 

SO 

316 

19 

2200 

38000 

12 

1  1000 

23.5 

1080 

10-inch 

1900 

224 

604 

33 

2500 

38000 

12 

12300 

24.7 

1148 

12-inch 

1900 

367 

1046 

58.3 

2500 

3800( 

10 

11600 

21.5 

12G9 

14-inch 

1906 

280 

1660 

58.5 

2150 

36000 

10 

11300 

20.9 

1302 

16-inch 

1895 

612 

2400 

139.3 

2150 

38000 

10 

12800 

22.4 

1373 

Mortar. 

10-inch 

1890 

34 

604 

33 

1150 

33000 

45 

11  SCO 

4S.1 

97.5 

12-inch 

1890 

54 

1016 

58.3 

1150 

33000 

45 

134CO 

52.7 

1055 

The  bursting  charges  given  in  the  table  are  for  shell.     The  bursting  charge 
for  a  shot  is  about  one  third  of  the  bursting  charge  for  a  shell  of  the  eaine  caliber. 

Other  data  concerning  the  seacoast  guns  will  be  found  in  the 
table  on  page  135. 

Seacoast  Guns. — The  seacoast  guns  and  mortars  are  con- 
structed as  shown  on  pages  237  and  238.  As  the  considerations 
that  limit  the  weights  of  the  guns  of  the  mobile  artillery  do  not 
apply  to  seacoast  guns  mounted  on  fixed  platforms,  and  as  with 
Icnger  guns  higher  muzzle  velocities  may  he  obtained  without 
increasing  the  maximum  pressure,  the  seacoast  guns  are  much 
longer,  in  calibers,  than  are  the  field  and  siege  pieces.  This  may 
be  noted  in  the  table  on  page  135. 

All  seacoast  guns  up  to  4.7  inches  in  caliber  use  fixed  ammuni- 
tion. In  guns  of  greater  caliber  the  projectile  is  inserted  first  and 
is  followed  by  the  powder  charge  made  up  in  one  or  more  bags. 
In  general  the  breech  mechanism  of  the  guns  using  fixed  ammuni- 
tion is  of  the  type  described  with  the  3-inch  field  gun.  Guns 
five  and  six  inches  in  caliber  are  provided  with  the  Bofors  of  simi- 
lar mechanism.  Larger  guns  have  the  cylindrical  slotted  screw 
mechanism  described  on  page  256. 

194.  Seacoast  Gun  Mounts.— The  mounts  for  the  seacoast  guns, 
commonly  called  carriages,  are  distinguished  as  barbette  or  dis- 
appearing carriages  according  as  they  hold  the  gun  always  ex- 
posed above  the  parapet  or  withdraw  the  gun  behind  the  parapet 


334  ORDNANCE  AND  GUNNERY. 

at  each  round  fired.  The  disappearing  carriage  has  the  advantage 
of  excellent  protection  for  the  carriage  and  gun  crew,  and,  for  guns 
of  the  larger  calibers,  the  added  advantage  of  greatly  increased 
rapidity  of  fire.  The  increased  rapidity  of  fire  is  due  to  the  lower- 
ing of  the  gun  to  a  height  convenient  for  loading,  so  that  the  heavy 
projectiles  and  charges  of  powder  need  not  be  lifted  in  loading. 
On  high  sites  the  disappearing  carriage  is  not  necessary  to  secure 
protection  for  the  gunners,  for  behind  the  parapets  the  gunners 
can  only  be  reached  by  high  angle  fire  from  the  enemy's  ship,  and 
on  account  of  the  excessive  strain  on  the  decks  that  would  accom- 
pany such  fire  guns  aboard  ship  are  not  so  mounted  that  they  can 
be  fired  at  high  angles.  Disappearing  carriages,  emplaced,  are 
more  costly  than  barbette  carriages,  but  the  advantage  of  the 
more  rapid  fire  from  the  disappearing  carriage  has  determined  its 
use  in  this  country  for  all  seacoast  guns  above  six  inches  in  caliber, 
on  high  sites  as  well  as  on  low  sites. 

Many  of  the  6-inch  guns  and  all  guns  below  six  inches  in  caliber 
are  mounted  on  barbette  carriages  provided  with  shields  of  armor 
plate  for  the  protection  of  the  gunners. 

Seacoast  guns  being  permanently  emplaced  the  weights  of  the 
gun  and  the  carriage,  and  simplicity  of  mechanism  in  both  gun  and 
carriage,  are  not  matters  of  such  importance  as  they  are  in  the 
field  and  siege  artillery.  We  consequently  find  adapted  to  the 
seacoast  guns  and  carriages  every  mechanism  that  will  assist  in 
increasing  the  rapidity  of  fire.  Fixed  ammunition  is  used  in  guns 
up  to  4.7  inches  in  caliber  and  its  use  will  probably  be  extended  to 
larger  calibers.  Experiments  are  being  made  with  mechanisms 
for  the  automatic  or  semi-automatic  opening  and  closing  of  the 
breech.  The  mechanisms  for  elevating  the  gun  and  for  traversing 
the  carriage  are  arranged  to  be  operated  from  either  side  of  the 
carriage,  and  in  the  carriages  for  the  larger  guns  provision  is  made 
for  the  operation  of  these  mechanisms  both  by  hand  and  by  electric 
power.  Sights  are  provided  on  both  sides  of  the  gun,  and  the 
operations  of  aiming  and  loading  may  proceed  together. 

Finally  the  magazines  and  shell  rooms  in  the  walls  of  the 
fortifications  are  so  arranged  with  regard  to  the  gun  emplacement, 
and  so  equipped,  as  to  insure  a  rapid  delivery  of  ammunition  to 
every  gun. 


ARTILLERY  OF   THE   UNITED  STATES  LAND  SERVICE.     335 

The  seacoast  gun  mounts  differ  for  guns  of  different  caliber. 
A  description  of  one  mount  of  each  distinct  type  will  follow  and 
will  serve  to  show  the  principles  that  govern  in  similar  construc- 
tions. 

GENERAL  CHARACTERISTICS. — In  general,  the  mount  consists  of 
a  fixed  base  bolted  to  the  concrete  platform  of  the  emplacement, 
and  of  a  gun-supporting  superstructure  resting  on  the  base  and 
capable  of  revolution  about  some  part  of  it.  The  superstructure 
supports,  in  addition  to  the  gun,  all  the  recoil  controlling  parts 
and  the  necessary  mechanisms  for  elevating,  traversing,  and  re- 
tracting the  gun. 

Fastened  to  the  fixed  base  or  to  the  platform  around  the  base 
is  an  azimuth  circle  graduated  to  half  degrees,  and  on  the  movable 
part  of  the  carriage  is  fixed  a  pointer,  with  vernier  reading  to 
minutes,  that  indicates  the  azimuth  angle  made  by  the  gun  with  a 
meridian  plane  through  its  center  of  motion.  ' 

The  gun,  supported  by  means  of  its  trunnions  on  the  super- 
structure of  the  carriage  or  contained  in  a  cradle  which  is  itself  so 
supported,  has  movement  in  elevation  about  the  axis  of  the  trun- 
nions. The  elevating  mechanisms,  or  the  sights,  are  provided 
with  graduated  scales  which  usually  indicate  the  range  correspond- 
ing to  each  position  of  the  gun. 

Protecting  guards  are  provided  wherever  necessary  for  the 
protection  of  the  gunners  against  accident,  or  for  the  protection 
of  the  mechanisms  of  the  carriage  against  the  entrance  of  dust  or 
water. 

195.  Pedestal  Mounts. — Seacoast  guns  up  to  six  inches  in 
caliber  are  mounted  in  barbette  on  carriages  similar  in  construction 
to  the  carriage  shown  in  Figs.  138  and  139. 

A  conical  pedestal  of  cast  steel,  p  Fig.  138,  is  bolted  to  the 
concrete  platform.  A  pivot  yoke  y  free  to  revolve  is  seated  in  the 
pedestal.  In  the  upwardly  extending  arms  of  the  pivot  yoke 
are  seats  for  the  trunnions  of  the  cradle  c.  The  gun  is  sup- 
ported and  slides  in  recoil  in  the  cradle.  The  weight  of  all 
the  revolving  parts  is  supported  by  a  roller  bearing  r  on 
a  central  boss  in  the  base  of  the  pedestal.  In  the  lower  rear 
portion  of  the  cradle  are  formed  a  central  recoil  cylinder  and  two 
spring  cylinders,  Fig.  139,  similar  to  the  corresponding  cyl- 


336 


ORDNANCE  AND  GUNNERY. 


inders  described  in  the  4.7-inch  siege  carriage,  but  much  shorter. 
As  the  seacoast  gun  mounts  are  firmly  bolted  to  platforms  and  as 

they  may  be  made  as  strong  as 
desired  without  limit  as  to 
weight,  these  mounts  will  stand 
much  higher  stresses,  without 
movement  or  rupture,  than  can 
be  imposed  on  a  wheeled 
carriage.  We  therefore  find 
that  shorter  recoil  is  allowed 
to  the  seacoast  guns  than  to 
the  lighter  field  and  siege 
guns.  Thus  the  recoil  of  the 
5-inch  gun  on  the  pedestal 
FIG.  138  mount  is  but  13  inches,  and 

of   the    6-inch  gun   15   inches, 

while  the  4.7-inch  siege  gun  recoils  66  inches  on  its  carriage  and 
the  3-inch  field  gun  45  inches. 

Bolted  to  the  arms  of  the  pivot  yoke,  on  each  side,  are  brack- 
ets to  which  are  attached  platforms  for  the  gunners.  The  plat- 
forms move  with  the  gun  hi  azimuth  and  carry  the  gunners  un- 
disturbed hi  the  operations  of  pointing  and  of  manipulating  the 
breech  mechanism. 

The  carriage  may  be  traversed  from  either  side.  The  shafts 
of  the  traversing  hand-wheels  extend  downward  toward  the 
pedestal  and  actuate  a  horizontal  shaft  held  in  bearings  on  the 
pivot  yoke.  A  worm  on  this  shaft  acts  on  a  circular  worm-wheel 
surrounding  the  top  of  the  pedestal,  t  Fig.  138. 

Elevation  is  given  by  the  upper  hand-wheel,  on  the  left  side 
only.  The  elevating  gear  is  supported  by  a  bracket  bolted  to  the 
platform  bracket  and  works  on  an  elevating  rack  attached  to  the 
cradle,  the  center  of  the  rack  being  in  the  axis  of  the  trunnions. 

The  traversing  rack,  or  worm-wheel,  surrounding  the  upper 
part  of  the  pedestal  is  held  to  the  pedestal  by  an  adjustable  friction 
band;  and  a  worm-wheel  in  the  elevating  gear,  contained  in  the 
gear  casing  fixed  to  the  elevating  bracket,  Fig.  139,  is  held  between 
two  adjustable  friction  disks.  These  friction  devices  are  so  ad- 
justed as  to  enable  the  gun  to  be  traversed  or  elevated  without 


ARTILLERY  OF   THE   UNITED  STATES  LAND  SERVICE.    337 

slipping  of  the  mechanism,  and  yet  to  permit  slipping  in  case  undue 
strain  is  brought  on  the  teeth  of  the  worm-wheels. 

A  shoulder  guard  is  attached  to  the  cradle  on  each  side  of  the 
gun  to  protect  the  gunners  from  injury  during  movement  of  the 
piece  in  recoil. 

Open  sights  and  a  telescopic  sight  are  seated  in  brackets  on 
the  cradle  on  each  side  of  the  gun.  Dry  batteries  in  two  boxes 
held  in  brackets  secured  to  the  platform  brackets  supply  electric 
power  for  firing  the  piece  and  for  lighting  the  electric  lamps  of  the 
sights. 

The  shield,  of  hardened  armor  plate,  4J  inches  thick,  is  fast- 
ened by  two  spring  supports  to  the  sides  of  the  pivot  yoke.  The 
bolt  holes  for  the  shield  support  are  seen  in  Fig.  139.  The  shield  is 
pierced  with  a  port  for  the  gun  and  with  two  sight  holes,  and  is 
inclined  at  an  angle  of  40  degrees  with  the  horizon,  see  Fig.  201. 

196.  The  Balanced  Pillar  Mount. — A  variation  of  the  mount 
just  described  is  found  in  the  balanced  pillar  mount,  also  called 
the  masking  parapet  mount.  This  mount  is  constructed  for  guns 
up  to  5  inches  in  caliber.  The  purpose  of  this  mount  is  to  afford  a 
means  of  withdrawing  the  gun,  when  not  in  use,  behind  the  para- 
pet and  out  of  the  view  of  the  enemy.  The  gun  is  withdrawn 
behind  the  parapet  only  after  the  firing  is  completed,  and  not 
after  each  round.  Guns  mounted  on  the  disappearing  carriages 
later  described  are  withdrawn  from  view  after  each  round  fired. 

The  construction  of  the  balanced  pillar  mount  will  be  under- 
stood from  Fig.  140.  The  pintle  yoke,  with  all  the  parts  sup- 
ported by  it,  rests  on  the  top  of  a  long  steel  cylinder  which  has 
movement  up  and  down  in  an  outer  cylinder.  The  base  of  the 
pintle  yoke  is  circular.  It  embraces  a  heavy  pintle  formed  on  the 
top  of  the  cylinder  and  rests  on  conical  rollers  which  move  on  a 
path  provided  on  the  cylinder  top.  Clips  attached  to  the  base  of 
the  pivot  yoke  engage  under  the  flanges  of  the  roller  path  and 
hold  the  top  carriage  to  the  cylinder. 

Imbedded  in  the  concrete  of  the  platform  is  the  outer  cast  iron 
cylinder  in  which  the  inner  cylinder  slides  up  and  down.  The 
weight  of  the  inner  cylinder  and  supported  parts  is  balanced  by 
lead  and  iron  counterweights  strung  on  a  central  rod  which  is 
connected  to  brackets  on  the  inside  of  the  inner  cylinder  by  three 


338 


ORDNANCE  AND  GUNNERY. 


chains.  The  pulleys  over  which  the  chains  pass  are  supported  on 
posts  that  pass  through  holes  in  the  counterweight  and  rest  in 
sockets  formed  in  the  bottom  of  the  cylinder.  For  lifting  and 
lowering  the  inner  cylinder  with  the  gun  and  top  carriage,  a  ver- 


tical toothed  rack  is  fixed  to  the  exterior  of  the  inner  cylinder.  A 
pinion  is  seated  in  bearings  provided  at  the  top  of  the  outer  cyl- 
inder and  engages  in  the  rack.  The  pinion  is  turned  by  means 
of  two  detachable  levers  mounted  on  the  ends  of  the  pinion  shaft. 


ARTILLERY  OF  THE   UNITED  STATES  LAND  SERVICE      339 

By  means  of  a  friction  clamp  the  pinion  is  made  to  hold  the  ele- 
vated carriage  against  any  sudden  downward  shock. 

The  construction  permits  a  vertical  movement  of  the  gun  and 
carriage  of  about  3|  feet. 

When  firing,  the  muzzle  of  the  gun  projects  over  the  parapet; 
and  before  lowering,  the  gun  is  turned  parallel  to  the  parapet. 

In  a  similar  mount  provided  for  3-inch  guns  the  outer  cylinder 
is  a  double  cylinder.  The  counterweight  is  annular  and  occupies 
the  space  between  the  two  cylinders  composing  the  double  outer 
cylinder.  The  lifting  levers  are  applied  directly  to  the  shaft  of 
one  of  the  chain  pulleys,  over  which  pass  the  chains  that  connect 
the  counterweight  to  brackets  on  the  outside  of  the  inner  cyl- 
inder. The  brackets  move  in  slots  provided  in  the  interior  of  the 
double  cylinder. 

197.  Barbette  Carriages  for  the  Larger  Guns. — Guns  from  8 
to  12  inches  in  caliber  are  mounted  in  barbette  on  carriages  similar 
in  construction  to  that  shown  in  Fig.  141.  The  carriages  are  made 


FIG.  141. 


principally  of  cast  steel,  all  the  larger  parts  with  the  exception  of 
the  base  ring  being  of  that  metal.  The  cast  iron  base  ring,  A 
Fig.  142,  has  formed  on  it  a  roller  path,  6,  on  which  rest  the  live 
conical  rollers  E  of  forged  steel.  The  rollers  are  flanged  at  their 
inner  ends  and  kept  at  the  right  distance  apart  by  outside  and 
inside  distance-rings  B.  The  central  upwardly  extending  cylinder 
c  forms  a  pintle  about  which  the  upper  carriage  revolves.  Em- 


340 


ORDNANCE    AND  GUNNERY. 


bracing  the  pintle  and  resting  on  the  rollers  is  an  upper  circular 
plate  called  the  racer.  Clips  attached  to  the  racer,  see  Fig.  141, 
and  engaging  under  the  flange  of  the  lower  roller  path  hold  the 
parts  together  under  the  shock  of  firing.  The  two  cheeks,  C 
Fig.  141,  of  the  chassis  are  cast  in  one  piece  with  the  racer  for  the 


FIG.  143. 


~u~  13 o — cnr 

FIG.  142. 


smaller  carriages  and  separately  for  the  larger  carriages,  and  are 
connected  together  by  transoms  and  strengthened  by  inner  and 

outer  ribs.  A  groove  or  recess  is 
formed  in  the  upper  part  of  each 
cheek,  see  Fig.  143,  for  the  series  of 
rollers  seen  in  Fig.  141,  on  which  the 
top  carriage  moves  in  recoil.  The 
axles  of  the  rollers  are  fixed  in  the 
walls  of  the  grooves  at  such  a  height 
that  the  tops  of  the  rollers  are  just 
above  the  top  of  the  chassis. 

The  top  carriage,  D  Fig.  141  and  a  Fig.  143,  rests  on  the  rollers 
and  is  held  to  the  chassis  by  means  of  the  clips  d,  Fig.  143.  The 
top  carriage  is  cast  hi  one  piece.  It  consists  of  two  side  frames 
united  by  a  transom  a  passing  under  the  gun.  The  side  frames 
contain  the  trunnion  beds  c  for  the  gun  trunnions  and  the  two 
recoil  cylinders  b.  The  piston  rods  of  the  recoil  cylinders  are 
held  in  lugs  formed  on  the  front  of  the  chassis. 

Elevation  from  minus  7  to  plus  18  degrees  is  given  by  means 
of  the  hand-wheel  seen  near  the  breech  of  the  gun,  Fig.  141,  or  by 
the  hand-wheel  just  under  the  top  carriage.  The  carriage  is 
traversed  by  means  of  the  crank  handle  in  front  of  the  chassis. 
Through  a  worm  and  worm-wheel  the  crank  actuates  a  sprocket- 
wheel  fixed  in  bearings  on  the  chassis.  A  chain  that  encircles  the 
base  ring  and  that  is  fast  to  the  base  ring  at  one  point  passes  over 


ARTILLERY  OF  THE   UNITED  STATES  LAND  SERVICE.     341 

the  sprocket-wheel.     When  the  sprocket-wheel  is  turned  it  pulls 
on  the  chain  and  causes  the  chassis  to  revolve. 

In  later  carriages  the  chain  is  replaced  by  a  circular  toothed 
rack  attached  to  and  surrounding  the  base  ring,  and  the  sprocket- 
wheel  is  replaced  by  a  gear  train  whose  end  pinion  meshes  in  the 
rack.  There  is  less  friction  and  less  lost  motion  with  this  construc- 
tion. 

The  shot  is  hoisted  to  the  breech  by  means  of  a  crane  attached 
to  the  side  of  the  carriage. 

When  the  gun  is  fired,  the  gun  and  top  carriage  recoil  to  the 
rear  on  the  rollers.  The  length  of  recoil  is  limited  by  the  length 
of  the  recoil  cylinder,  and  on  this  type  of  carriage  is  about  five 
calibers.  The  recoil  is  absorbed  partly  in  lifting  the  gun  and  top 
carriage  up  the  inclined  chassis  rails  and  partly  by  friction,  but 
principally  by  the  resistance  of  the  recoil  cylinders,  as  explained  in 
the  chapter  on  recoil. 

On  cessation  of  the  recoil  the  gun  returns  to  battery  under  the 
action  of  gravity,  the  inclination  of  the  chassis  rails,  four  degrees, 
being  greater  than  the  angle  of  friction. 

198.  Disappearing  Carriages. — The  importance  of  the  func- 
tion of  the  heavy  seacoast  guns,  the  difficulty  in  the  way  of  quick 
or  extensive  repairs  to  their  mounts,  the  great  cost  of  the  guns 
and  their  carriages,  are  all  considerations  that  point  to  the  desira- 
bility of  giving  to  these  guns  and  carriages  the  greatest  amount 
of  protection  practicable. 

The  guns  are  therefore  emplaced  in  the  fortifications  behind 
very  thick  walls  of  concrete,  which  are  themselves  protected  in  front 
by  thick  layers  of  earth.  Additional  protection  is  obtained  by 
mounting  the  guns  on  carriages  which  withdraw  the  guns  from 
their  exposed  firing  position  above  the  parapet  to  a  position 
behind  the  parapet  and  below  its  crest,  where  the  gun  and  every 
part  of  the  carriage  except  the  sighting  platforms  and  sight  stand- 
ards are  protected  from  a  shot  that  grazes  the  crest  at  an  angle  of 
seven  degrees  with  the  horizontal. 

An  additional  and  very  important  advantage  gained  by  the 
use  of  these  carriages  is  the  increased  rapidity  of  fire  obtained 
from  the  guns  mounted  upon  them.  The  guns  in  their  lowered 
positions  are  at  a  convenient  level  for  loading,  and  the  time  and 


342  ORDNANCE  AND  GUNNERY. 

labor  that  must  be  expended  in  lifting  the  heavy  projectiles  and 
powder  charges  to  the  breech  of  a  gun  of  the  same  caliber  mounted 
in  barbette  are  practically  eliminated. 

1 2 -inch  Disappearing  Carriage,  Model  1901. — The  annular  base 
ring,  6  Fig.  144,  surrounds  a  well  left  in  the  concrete  of  the  em- 
placement. The  racer  a  rests  on  live  rollers  on  the  base  ring  and 
is  pintled  on  a  cylinder  formed  by  the  inner  wall  of  the  base  ring- 
The  racer  supports  the  superstructure  as  in  the  carriage  just  de- 
scribed. It  is  held  to  the  base  ring  by  clips  c,  which  engage  under 
a  flange  on  the  inside  of  the  pintle.  A  working  platform,  or  floor, 
of  steel  plates  is  fixed  to  brackets  x  fastened  to  the  racer,  and 
moves  with  the  carriage  in  azimuth. 

The  forward  ends  of  the  chassis  cheeks  are  continued  upward, 
and  on  the  inside  of  the  cheeks  and  of  the  upward  extensions  are 
formed  vertical  guideways  for  the  crosshead  k,  from  which  the 
counterweight  w  is  suspended. 

GUN  LIFTING  SYSTEM. — The  top  carriage,  similar  in  construc- 
tion to  that  of  the  barbette  carriage,  rests  on  flanged  live  rollers 
which  roll  on  the  rails  of  the  chassis.  The  rollers  are  connected 
together  by  side  bars  in  which  the  axles  of  the  rollers  are  fixed. 

The  gun  levers  I  are  trunnioned  in  the  trunnion  beds  of  the  top 
carriage.  They  support  the  gun^  between  their  upper  ends,  and 
between  their  lower  ends,  the  crosshead  k  from  which  the  counter- 
weight is  suspended. 

The  crosshead  is  provided  with  clips  that  engage  the  vertical 
guides  formed  on  the  inside  of  the  chassis  cheeks.  Cut  on  the 
front  faces  of  the  clips  of  the  crosshead  are  ratchet  teeth  in  which 
pawls  p  engage  to  hold  the  counterweight  up  after  the  gun  has 
recoiled.  The  pawls  are  pivoted  on  the  chassis.  Levers  v  pivoted 
on  the  ends  of  a  shaft  across  the  front  of  the  chassis  serve  as  means 
for  releasing  the  pawls  when  it  is  desired  to  put  the  gun  in 
battery. 

The  counterweight  consists  of  102  blocks  of  lead  of  varying 
size,  weighing  approximately  164,700  pounds.  It  is  piled  on  the 
bottom  plate  m,  which  is  suspended  by  four  stout  rods  from  the 
crosshead.  The  preponderance  of  the  counterweight  may  be  ad- 
justed, within  limits,  by  the  addition  or  removal  of  "small  weights 
at  the  top. 


ARTILLERY  OF  THE   UNITED  STATES  LAND  SERVICE.     343 


344  ORDNANCE  AND  GUNNERY. 

199.  ELEVATING  SYSTEM. — The  gun  elevating  system  consists 
of  the  band  n  dowelled  to  the  gun  and  provided  with  trunnions 
that  are  engaged  by  the  forked  ends  of  the  elevating  arm  h.  The 
elevating  arm  has  at  its  lower  end  a  double  ended  pin  which  ro- 
tates in  bearings  in  the  elevating  slide  s.  The  elevating  slide  has  a 
movement  up  and  down  on  an  inclined  guideway  machined  on  the 
rear  face  of  the  rear  transom.  Movement  is  given  to  the  slide  by 
means  of  a  large  axial  screw  on  which  the  slide  moves  as  a  nut 
prevented  from  turning.  The  screw  is  turned  by  gearing  on  the 
shaft  e  actuated  by  hand-wheels  outside  the  carriage.  In  order 
to  counterbalance  the  weight  of  the  elevating  arm  and  band,  and 
to  equalize  the  efforts  required  in  elevating  and  depressing  the 
gun,  a  wire  rope  passes  from  the  elevating  slide  over  pulleys  and 
supports  a  counterbalancing  weight  g.  The  gun  moves  in  eleva- 
tion from  minus  5  degrees  to  plus  10  degrees. 

TRAVERSING  SYSTEM. — Crank-handles  on  the  traversing  shaft 
t  actuate,  through  gearing,  a  vertical  shaft  carrying  at  its  lower 
end  a  pinion  o  which  works  in  a  circular  rack  on  the  inside  of  the 
base  ring.  In  a  convenient  position  on  the  racer  near  the  azimuth 
pointer  is  placed  the  lever  of  a  traversing  brake,  not  shown,  which 
works  against  the  base  ring.  By  its  means  traversing  is  retarded 
as  the  carriage  approaches  any  desired  azimuth. 

RETRACTING  SYSTEM. — Means  are  provided  to  bring  the  gun 
down  from  its  firing  position  when  for  any  reason  it  has  been  ele- 
vated into  battery  and  not  fired.  Detachable  crank-handles 
mounted  on  the  ends  of  the  shaft  r  turn  tw-o  winding  drums  on 
the  shaft  u  inside  the  chassis.  A  wire  rope  y  leads  from  each 
drum  around  a  pulley  at  the  rear  end  of  the  chassis  to  the  top  of 
the  gun  lever,  a  loop  in  the  end  of  the  rope  engaging  over  the  hook 
of  the  lever. 

SIGHTING  SYSTEM. — Elevated  platforms  are  provided  on  each 
side  of  the  carriage.  The  telescopic  sight,  see  Fig.  145,  is  mounted 
above  the  left  platform  on  a  hollow  standard  that  rises  from  the 
floor  of  the  racer.  A  vertical  rod  passing  through  the  standard  is 
connected  at  the  top  to  a  pivoted  arm  carrying  the  sight,  and  at 
the  bottom  the  rod  is  so  geared  to  the  elevating  shaft  that  the 
same  movement  in  elevation  is  given  to  the  sight  arm  as  is  given 
to  the  gun.  Within  reach  of  the  gunner  at  the  sight  are  two 


ARTILLERY  OF  THE   UNITED  STATES  LAND  SERVICE.     345 

crank-handles,  at  the  upper  ends  of  vertical  shafts,  by  means  of 
which  the  gunner  has  electric  control  of  the  elevating,  traversing, 
and  retracting  mechanisms. 

Trials  are  being  made  of  the  panoramic  sight  fitted  to  disap- 
pearing carriages.  The  vertical  tube  of  the  sight  is  made  very 
long  and  the  sight  is  attached  to  the  side  of  the  carriage  in  such  a 
position  that  the  eye  piece  is  convenient  to  the  gunner  standing 
on  the  racer  platform,  while  the  head  piece  of  the  sight  is  above 
the  parapet. 

OPERATION. — The  operation  of  the  carriage  for  firing  is  as 
follows.  The  gun  is  loaded  in  its  retracted  position,  Fig.  145, 
being  held  in  that  position  by  the  pawls  p  engaged  in  the  notches 
on  the  crosshead  k.  After  the  gun  is  loaded  the  tripping  levers  v 
are  raised,  releasing  the  pawls  from  the  notches  in  the  crosshead. 
The  counterweight  falls  and  the  top  carriage  moves  forward  on 
its  rollers,  the  last  part  of  its  motion  being  controlled  by  the 
counter-recoil  buffers  in  the  recoil  cylinders,  so  that  the  top  carriage 
comes  to  rest  without  shock  on  the  chassis.  By  the  movement  of 
the  gun  levers  the  gun  is  lifted  to  its  elevated  position  above  the 
parapet. 

When  the  piece  is  fired  the  movements  are  reversed  in  direc- 
tion. The  recoil  forces  the  gun  to  the  rear,  the  top  carriage  rolls 
back  on  the  chassis  rails  and  the  counterweight  rises  vertically 
under  the  restraint  of  the  guides  engaged  by  the  crosshead. 

In  the  movement  either  way  the  upper  end  of  the  gun  lever  de- 
scribes an  arc  of  an  ellipse.  The  path  of  the  muzzle  of  the  gun, 
indicated  in  Fig.  144,  is  affected  by  the  constraint  of  the  elevating 
arm.  The  ellipse  is  the  most  favorable  figure  to  follow  in  the 
movement  of  a  gun  on  a  disappearing  carriage.  From  the  firing 
position  the  movement  of  the  gun  is  at  first  almost  horizontally 
backward,  and  the  movement  downward  occurs  principally  in  the 
latter  part  of  the  path.  Therefore  the  carriage  that  moves  the 
gun  in  an  elliptical  path  can  be  brought  nearer  to  the  parapet  and 
thus  receive  better  protection  than  any  other  carriage. 

The  recoil  is  controlled  principally  by  the  recoil  cylinders,  and 
the  shock  at  the  cessation  of  motion  is  mitigated  by  two  buffers  / 
which  receive  the  ends  of  the  gun  levers.  The  buffers  are  com- 
posed of  steel  plates  alternating  with  sheets  of  balata. 


346  ORDNANCE  AND  GUNNERY. 

Balata  is  a  substance  that  resembles  hardened  rubber.  It  has 
not  as  great  elasticity  as  rubber  but  does  not  deteriorate  as  rapidly 
under  exposure  to  the  weather. 

200.  Modification  of  the  Recoil  System. — In  the  chapter  on 
recoil  it  was  pointed  out  that  there  is  a  disadvantage  in  having  the 
control  of  the  counter  recoil  in  the  same  hydraulic  cylinders  that 
control  the  recoil.     The  adjustment  of  the  counter-recoil  system 
affects  the  adjustment  of  the  recoil  system. 

It  will  also  be  observed  in  the  carriage  just  described  that  in 
the  latter  part  of  the  movement  in  recoil  the  gun  is  moving 
almost  vertically  downward.  Consequently  the  movement  of  the 
top  carriage  to  the  rear  is  very  slight  during  this  part  of  the  recoil, 
and  the  slight  movement  affords  little  opportunity  for  the  close 
control  by  the  recoil  cylinders  of  the  final  movement  of  the  gun. 
But  it  is  in  the  last  part  of  the  recoil  that  complete  control  of  the 
movement  of  the  gun  is  most  desirable,  in  order  that  the  gun  may 
be  brought  to  rest  at  any  desired  position  for  loading,  and  without 
shock  to  the  carriage. 

While  the  movement  of  the  top  carriage  is  least  rapid  at  the 
latter  end  of  recoil  the  counterweight  has  then  its  most  rapid  move- 
ment. Therefore  a  recoil  cylinder  fixed  so  as  to  move  with  the 
counterweight  will  afford  the  best  control  of  the  final  movement 
of  the  gun. 

The  top  carriage  has  its  most  rapid  movement  at  the  latter 
part  of  the  movement  of  the  gun  into  battery,  while  the  counter- 
weight has  its  least  rapid  movement  at  that  time.  The  control 
of  the  counter  recoil  is  therefore  best  effected  through  the  top 
carriage. 

By  retaining  therefore,  to  act  on  the  top  carriage,  recoil  cyl- 
inders adapted  for  the  control  of  the  counter  recoil  only,  and  by 
adding  to  the  counterweight  a  cylinder  adapted  for  control  of  the 
recoil,  we  will  obtain  the  advantage  of  completely  separating  the 
two  systems,  thus  making  them  capable  of  independent  adjust- 
ment, and  the  advantage  of  obtaining  from  each  system  the 
greatest  control  of  the  movement  to  which  it  is  applied. 

201.  6-inch  Experimental    Disappearing    Carriage,  Model 
1905. — The  modification  of  the  recoil  system  as  above  indicated 
has  been  applied  to  a  6-inch  experimental  carriage. 


ARTILLERY  OF  THE   UNITED  STATES  LAND  SERVICE.     347 

The  recoil  cylinder  is  held  in  the  center  of  the  counterweight, 
Fig.  146.  The  lower  end  of  the  piston  rod  is  fixed  in  the  lower 
member  d  of  a  frame  whose  sides  /  are  bolted  to  the  bottom  of  the 
racer  a,  as  shown  hi  the  left  and  rear  views.  Grooves  cut  in  the 
walls  of  the  recoil  cylinder  permit  the  flow  of  the  liquid  from  one 
side  of  the  piston  to  the  other.  For  the  regulation  of  the  extent 
of  the  recoil,  and  therefore  of  the  height  of  the  gun  when  in  load- 
ing position,  two  diagonal  channels  pass  through  the  center  of  the 
piston  head  from  one  face  to  the  other,  and  the  flow  through  them 
is  controlled  by  a  conical  valve  enclosed  in  the  upper  piston  rod, 
which  is  hollow.  The  stem  of  the  valve  projects  above  the  end  of 
the  piston  rod. 

The  counter  recoil  is  checked  by  the  short  cylinders  s  mounted 
on  each  chassis  rail  in  front  of  the  top  carriage.  The  pistons  of 
the  counter-recoil  cylinders  are  not  provided  with  apertures  for 
the  flow  of  the  liquid  from  one  side  of  the  piston  to  the  other,  but 
the  flow  of  the  liquid  takes  place  through  the  pipes  p  which  are  led 
from  both  cylinders  to  a  valve  v,  by  which  the  area  of  orifice  is 
controlled  and  through  which  the  pressure  in  the  two  cylinders  is 
equalized.  The  pressure  in  the  counter-recoil  cylinders  does  not 
exceed  500  pounds  per  square  inch,  while  the  pressure  in  the  recoil 
cylinder  is  1800  pounds. 

As  the  top  carriage  comes  into  battery  the  front  of  the  carriage 
strikes  the  rear  end  o  of  the  piston  rod  and  forces  the  piston  through 
the  cylinder  against  the  liquid  resistance  and  against  the  action 
of  springs  g  mounted  on  each  side  of  the  cylinder.  The  springs 
act  on  central  rods  connected  to  the  forward  end  of  the  piston, 
and  as  the  top  carriage  moves  from  battery  the  springs  move  the 
piston  to  the  rear  in  position  to  be  acted  on  by  the  top  carriage 
as  it  comes  back  into  battery. 

There  are  other  points  of  difference  between  this  carriage  and 
the  carriage  last  described. 

The  retraction  of  the  gun  from  the  firing  position  is  accom- 
plished without  the  use  of  wire  ropes  by  the  vertical  racks  6,  shown 
hi  the  left  and  rear  views,  attached  to  bars  that  connect  the  cross- 
head  k  and  the  bottom  section  m  of  the  counterweight.  The  end 
pinions  5  of  two  trains  of  gears,  one  on  each  side,  mesh  in  the  rack, 
the  gear  trains  being  actuated  by  the  cranks  on  the  shaft  r.  The 


348 


ORDNANCE  AND  GUNNERY. 


View-  Rear  View. 

FIG.  146.— 6-inch  Experimental  Disappearing  Carriage,  Model  1905. 


ARTILLERY  OF  THE  UNITED  STATES  LAXD  SERVICE.     349 

retracting  mechanism  is  partially  shown  in  the  smaller  views. 
The  parts  are  similarly  numbered  in  all  the  figures.  The  mechan- 
ism is  thrown  out  of  gear  when  not  in  use. 

The  rollers  of  the  top  carriage  are  geared  to  the  top  carriage 
so  that  they  are  compelled  to  move  with  ihe  top  carriage  and 
there  can  be  no  slipping  of  the  top  carriage  on  the  rollers.  In 
present  service  carriages  this  slipping  sometimes  occurs  as  the  gun 
recoils,  so  that  on  counter  recoil  the  rollers  reach  their  position  in 
battery  before  the  top  carriage,  and  prevent  the  top  carriage  from 
coming  fully  into  battery. 

The  sight  standard  is  moved  to  the  front  of  the  chassis  in  order 
to  get  better  protection  for  the  gunner,  for  the  sight,  and  for  the 
elevating  and  traversing  mechanisms  under  control  of  the  gunner. 
Through  the  upper  hand-wheel  e  and  the  shafts  and  gears  also 
marked  e  the  gunner  has  control  of  the  elevating  mechanism; 
and  through  another  hand-wheel  at  his  right  hand,  covered  by  the 
wheel  e  in  the  figure,  and  the  shafts  and  gears  marked  t  he  con- 
trols the  traversing  mechanism. 

Firings  from  this  6-inch  carriage  have  shown  that  the  gunner 
on  the  sighting  platform  is  so  near  the  muzzle  of  the  gun  that  he 
is  injuriously  affected  by  the  blast.  The  sighting  platforms  will 
therefore  be  removed  to  the  rear  end  of  the  carriage,  in  which 
position  they  will  also  afford  means  of  access  to  the  breech  when 
the  gun  is  up. 

202.  Seacoast  Mortars. — The  thick  armored  sides  of  ships  of 
war  protect  the  ships  to  a  greater  or  less  extent  against  the  direct 
fire  from  high  powered  guns.  The  great  weight  of  armor  that 
would  be  required  for  complete  deck  protection  is  prohibitive. 
The  decks  of  war  ships  are  therefore  thin  and  practically  un- 
armored,  the  heaviest  protective  deck  on  any  battleship  being  not 
more  than  two  inches  thick  over  the  flat  part.  The  decks  there- 
fore offer  an  attractive  target. 

As  the  elevation  above  sea  level  of  the  sites  of  the  guns  in  most 
fortifications  is  not  sufficient  to  permit  direct  fire  against  the 
decks,  there  are  provided  for  use  against  this  target  the  12-inch 
seacoast  mortars,  short  guns  so  mounted  that  they  can  be  fired  at 
high  angles  only.  The  heavy  projectiles  fired  from  these  guns 
carry  large  bursting  charges  of  high  explosive.  Descending 


350 


ORDNANCE  A.VD  GUNNERY. 


almost  vertically  on  the  deck  of  a  ship  they  easily  overcome  the 
slight  resistance  offered,  and  penetrating  to  the  interior  of  the 
ship  burst  there  with  enormous  destructive  effect. 

The  mortar  carriages  permit  firing  only  at  angles  of  elevation 
between  45  and  70  degrees.  With  a  fixed  charge  of  powder  a  lim- 
ited range  only  would  be  covered  by  fire  between  these  angles. 
Charges  of  several  different  weights  are  therefore  used  in  the 
mortars.  With  each  charge  a  certain  zone  in  range  may  be  cov- 
ered by  the  fire,  and  the  charges  are  so  fixed  that  the  range  zones 
overlap.  Any  point  within  the  limits  of  range  may  thus  be 
reached  by  the  projectile.  The  least  range  with  the  smallest 
charge  provided  is  about  a  mile  and  a  half.  Mortar  batteries  are 
therefore  usually  erected  at  not  less  than  this  distance  from  the 
channels  or  anchorages  that  are  under  their  protection. 

The  12-inch  Mortar  Carriage, -Model  1896. — The  construction 
of  the  12-inch  mortar  carriage,  model  1896,  will  be  understood 
from  Fig.  147.  The  mortar  is  supported  by  the  upper  ends  of  the 


FIG.  147. 

two  arms  of  a  saddle  d  which  is  hinged  on  a  heavy  bolt  to  the 
front  of  the  racer.  The  arms  of  the  saddle  are  connected  by  a 
thick  web.  Extending  across  under  the  web  is  a  rocking  cap- 
piece,  c,  against  which  five  columns  of  coiled  springs  act,  sup- 
porting the  gun  in  its  position  in  battery  and  returning  it  to  bat- 
tery after  recoil. 


ARTILLERY  OF  THE   UNITED  STATES  LAND  SERVICE.     351 


The  lower  ends  of  the  springs  rest  in  an  iron  box  trunnioned  in 
two  brackets  bolted  to  the  bottom  of  the  racer.  The  box  oscil- 
lates as  required  during  the  movement  of  the  saddle  in  recoil  and 
counter  recoil.  Holes  in  the  bottom  of  the  box  and  in  the  cap- 
piece  and  saddle  web  permit  the  ends  of  the  rods  on  which  the 
springs  are  strung  to  pass  through  during  the  movement. 

The  recoil  cylinders  h  are  trunnioned  in  bearings  fixed  to  the 
top  of  the  racer.  Bolted  to  the  top  of  each  cylinder  is  a  frame  / 
which  serves  as  a  guide  for  the  crosshead  o  at  the  upper  end  of 
the  piston  rod.  The  crosshead  embraces  the  stout  pin  r  which 
extends  outward  from  the  trunnion  of  the  mortar  and  communi- 
cates the  motion  of  the  piece  in  recoil  to  the  piston  rod. 

The  provision  for  the  flow  of  liquid  in  the 
recoil  cylinder  from  one  side  of  the  piston  to 
the  other  differs  in  this  carriage  from  that 
described  in  other  carriages.  A  small  cyl- 
inder, A  Fig.  148,  is  formed  outside  the  re- 
coil cylinder  proper,  H.  Holes  a,  bored 
through  the  dividing  wall,  form  passages 
through  which  the  oil  may  pass  from  the 
front  of  the  piston  to  the  rear.  The  piston 
head  in  its  movement  closes  the  holes  suc- 
cessively. Thus  as  the  velocity  of  recoil  de- 
creases the  area  open  to  the  flow  of  the  liquid 
is  reduced.  The  area  of  aperture  is  also 
regulated  by  screw  throttling  plugs  6  that 
are  seated  in  the  outer  wall  of  the  small  cyl- 
inder. These  plugs  have  stems  of  different 
diameters,  and  are  used  to  partially  or 
wholly  close  any  of  the  passages  in  the 
proper  regulation  of  the  recoil.  The  recoil 
cylinders  on  each  side  of  the  carriage  are  con- 
nected by  the  equalizing  pipe  p. 

The  counter  recoil  is  checked  and  the  gun 
brought  into  battery  without  shock  by  the  FlG  148 

counter-recoil  buffer  s,  an  annular  projection 
formed  on  the  cylinder  head  surrounding  the  piston  rod.    The  buffer 
enters,  with  a  small  clearance,  an  annular  cavity  in  the  head  of 


352 


ORDNANCE  A-\D  GUNNERY. 


the  piston,  and  the  liquid  in  the  cavity  escapes  slowly  through  the 
clearance.  As  an  added  precaution  against  shock  when  the  gun 
returns  to  battery,  buffer  stops  composed  of  alternate  layers  of 
balata  and  steel  plates  are  held  between  the  crosshead  guides  of 
the  frame  /,  Fig.  147,  under  the  cap. 

The  gun  is  elevated  by  the  mechanism  shown  mounted  on  the 
saddle,  Fig.  147,  and  traversed  by  means  of  the  crank  shaft  and 
mechanism  supported  in  a  vertical  stand  on  the  racer.  A  pinion 
p  on  the  end  of  a  vertical  shaft  engages  in  a  circular  rack  bolted 
to  the  inner  surface  of  the  base  ring. 

The  movement  of  the  saddle  in  recoil  causes  the  gun  to  rotate 
on  its  trunnions.  To  prevent  excessive  rotation  of  the  gun  and 
excessive  strain  on  the  elevating  mechanism,  a  friction  collar  is 
provided  in  the  large  gear  wheel  of  the  elevating  mechanism. 
The  collar  slips  in  the  gear  wheel  when  the  strain  is  ex- 
cessive. 

For  determining  elevation,  a  quadrant,  similar  to  the  gun- 
ner's quadrant  described  in  the  chapter  on  sights,  is  permanently 
attached  to  a  seat  prepared  on  the  right  rim  base  of  the  mortar. 


149. 


203.  The  12-inch  Mortar  Carriage,  Model  1891. — The  12-inch 
mortar  carriage,  model  1891,  on  which  many  12-inch  mortars  are 
mounted  in  our  fortifications,  is  shown  in  Figs.  149  and  150. 


ARTILLERY  OF   THE    UNITED   STATES  LAND  SERVICE.     353 


-r 


The  spring  cylinders  E  are  formed  in  the  vertical  cheeks  bolted 
to  the  racer.  Inside  the  cheeks  are  inclined  guideways  for  sliding 
crossheads  G.  The  crossheads  receive  the 
trunnions  of  the  gun.  The  pistons  h  of  the 
recoil  cylinders  project  downward  from  the 
crossheads  and  enter  the  recoil  cylinders  H 
attached  to  the  lower  parts  of  the  spring  cyl- 
inders. The  recoil  cylinders  are  of  the  type 
shown  in  Fig.  148.  The  crosshead  G  has  at  its 
upper  end  an  arm,  r  Fig.  150,  which  projects 
outwardly  into  the  spring  cylinder  and  carries 
at  its  outer  end  the  adjusting  screw  k,  which 
rests  on  top  of  the  column  of  springs.  The 
springs  are  compressed  when  the  gun  recoils, 
and  return  the  gun  to  battery  on  the  cessation 
of  recoil.  By  means  of  the  adjusting  screw  k 
the  height  of  the  trunnion  carriages  G  may  be 
adjusted  to  bring  the  mortar  to  the  proper 
height  for  loading. 

The  hand-wheel  g,  Fig.  149,  works  the  shot 
hoist  a,  by  means  of  which  the  shot  is  lifted  to 
the  breech  of  the  gun  for  loading. 

204.  Subcaliber  Tubes. — For  the- purpose  of 
enabling  troops  to  become  familiar  with  the 
operation  of  the  guns  and  carriages  by  actual 
firing,  yet  without  the  expense  attendant  upon 
the  use  of  the  regular  ammunition,  there  are  provided  for  use 
inside  the  various  service  guns  smaller  guns  or  gun  barrels  called 
subcaliber  tubes.  These  are  seated  in  the  bores  of  the  larger  guns 
in  such  position  that  the  breech  of  the  subcaliber  tube  is -just  in 
front  of  the  breech  block  of  the  gun  when  closed.  The  sub- 
caliber  tube  is  loaded  with  fixed  ammunition  arranged  to  be  fired 
by  the  firing  mechanism  of  the  larger  gun.  Three  calibers  of  sub- 
caliber  tubes  are  provided:  one  of  0.30-inch  caliber,  using  the 
small  arm  cartridge,  for  guns  that  use  fixed  ammunition;  one  of 
1. 475-inch  caliber,  using  1-pounder  ammunition,  for  use  in  all 
guns  5  inches  or  more  in  caliber;  and  one  of  75  mm.  (2.95  inches) 
caliber,  using  18-pounder  ammunition,  for  use  in  the  12-inch  mortar. 


FIG.  150. 


354 


ORDNANCE  AND  GUNNERY. 


For  those  guns  that  use  fixed  ammunition  the  30-caliber  sub- 
caliber  tube,  a  30-caliber  rifle  barrel,  is  fixed  in  a  metal  mounting 
that  has  the  shape  and  dimensions  of  the  complete  cartridge  used 
in  the  piece.  Fig.  151  shows  the  subcaliber  tube  for  the  3-inch 
rifle. 


FIG.  151. 

The  30-caliber  small  arm  cartridge  is  inserted  in  the  barrel  6 
and  is  fired  by  the  percussion  firing  mechanism  of  the  piece.  It 
is  extracted,  far  enough  to  be  grasped  by  the  hand,  by  the  ex- 
tractor, two  bowed  springs  s  which  are  under  compression  when 
the  small  arm  cartridge  is  forced  to  its  seat  by  the  breech  block 
of  the  gun.  A  special  primer  is  used  in  the  small  arm  cartridge, 
strong  enough  to  withstand  without  puncture  the  heavy  blow  of 
the  firing  pin  of  the  gun. 

The  head  of  the  subcaliber  cartridge  is  permitted  longitudinal 
movement  in  the  body  in  order  to  allow  for  expansion  of  the  30- 
caliber  barrel  in  firing. 


FIG.  152. 

The  1-pounder  tube  is  provided  with  different  fittings  to  adapt 
it  to  the  particular  gun  in  which  it  is  to  be  used.  It  is  fitted  in 
the  gun  in  the  manner  shown  in  Fig.  152,  which  represents  the 
75  mm.  subcaliber  tube  in  the  12-inch  mortar. 

The  75  mm.  tube  is  a  gun  similar  to  the  mountain  gun,  without 


ARTILLERY  OF  THE  UNITED  STATES  LAND  SERVICE.     355 

its  breech  mechanism.  The  cartridges  for  the  mountain  gun  are 
used  in  it. 

The  wheel-shaped  fittings,  called  adapters,  are 'screwed  on  the 
gun.  The  front  adapter  fits  against  the  centering  slope  in  the 
bore  for  the  band  of  the  projectile.  The  outer  rim  of  the  rear 
adapter  is  cut  through  at  the  top  and  the  rim  is  expanded  against 
the  sides  of  the  bore  by  the  wedge  w,  which  is  forced  between  the 
parts  of  the  rim  by  means  of  the  screw  seated  in  one  of  them. 
The  tube  is  prevented  from  turning  in  the  adapters  by  the  clamp 
screw  c. 

The  firing  mechanism  of  the  guns  in  which  the  two  larger 
subcaliber  tubes  are  used  is  not  of  the  percussion  type.  The 
camion  cartridges  used  in  these  two  tubes  are  therefore  provided 
with  the  110-gram  igniting  primer,  described  in  the  chapter  on 
primers,  in  place  of  the  usual  percussion  primer.  The  igniting 
primer  in  the  cartridge  is  ignited  by  the  flame  from  the  ordinary 
primer  seated  in  the  rear  end  of  the  breech  mechanism  of  the 
gun. 

Drill  Cartridges,  Projectiles,  and  Powder  Charges. — For  ordi- 
nary use  at  drill,  without  firing,  dummy  cartridges  are  provided 
for  guns  that  use  fixed  ammunition,  and  dummy  projectiles  and 
powder  charges  for  other  guns.  The  dummies  have  the  dimen- 
sions and  weights  of  the  parts  they  represent. 

The  drill  cartridge  for  guns  using  fixed  ammunition  are  hollow 
bronze  castings,  Fig.  153,  of  the  shape  of  the  service  cartridge 


FIG.  153. 

loaded  with  shrapnel.  For  the  instruction  of  cannoneers  in  fuse 
setting  there  is  fitted  at  the  head  of  the  cartridge  a  movable  ring 
graduated  in  the  same  manner  as  the  time  scale  on  the  combina- 
tion time  and  percussion  fuse. 

Drill  projectiles,  for  guns  separately  loaded,  are  of  the  con- 
struction shown  in  Fig.  154.  A  bronze  band,  6,  is  inset  at  the 
bourrelet  to  prevent  wearing  of  the  rifling  in  the  gun  by  frequent 


356 


ORDNANCE  AXD  GUNNERY. 


insertion  of  the  projectile.  The  rotating  band  r,  made  in  two  or 
more  sections  with  spaces  between,  is  pressed  to  the  rear  on  a 
sloping  seat  by  springs  s.  When  the  projectile  is  rammed  with 
force  into  the  gun  the  band  is  likely  to  stick  in  its  seat  and  thus 
to  resist  efforts  to  withdraw  the  projectile.  The  method  of  at- 
tachment of  the  band  is  for  the  purpose  of  affording  a  means  of 
readily  overcoming  this  resistance.  The  extractor,  a  hook  on  the 


FIG.  154. 


end  of  a  pole,  is  engaged  over  the  inner  lip  I.  A  pull  on  the  pole 
will,  if  the  band  is  stuck,  first  move  the  remainder  of  the  projectile 
to  the  rear  until  it  strikes  and  dislodges  the  band. 

The  dummy  powder   charge,  Fig.  155,  circular   in  section,  is 


FIG.  155. 


made  up  of  a  core  of  metal  surrounded  by  disks  of  wood,  the 
whole  covered  with  canvas.  The  parts  are  assembled  by  means 
of  a  central  bolt.  An  inner  lip  /  formed  in  the  hollow  metal  base 
piece  is  engaged  by  the  hook  of  the  extractor. 


CHAPTER  IX. 
EXTERIOR  BALLISTICS. 

205.  Definitions. — Exterior  Ballistics  treats  of  the  motion  of  a 
projectile  after  it  has  left  the  piece. 

In  the  discussions  the  dimensions  of  the  gun  are  considered 
negligible  in  comparison  with  the  trajectory. 

The  Trajectory,  bdf,  Fig.  156,  is  the  curve  described  by  the 
center  of  gravity  of  the  projectile  in  its  movement. 


FIG.  156. 

The  Range,  bf,  is  the  distance  from  the  muzzle  of  the  gun  to 
the  target. 

The  Line  of  Sight,  abf,  is  the  straight  line  passing  through 
the  sights  and  the  point  aimed  at. 

The  Line  of  Departure,  be,  is  the  prolongation  of  the  axis  of 
the  bore  at  the  instant  the  projectile  leaves  the  gun. 

The  Plane  of  Fire,  or  Plane  of  Departure,  is  the  vertical  plane 
through  the  line  of  departure. 

357 


358  ORDNAXCE   AND  GUNNERY. 

The  Angle  of  Position,  s,  is  the  angle  made  by  the  line  of  sight 
with  the  horizontal. 

The  Angle  of  Departure,  <f>,  is  the  angle  made  by  the  line  of 
departure  with  the  line  of  sight. 

The  Quadrant  Angle  of  Departure,  <£+£,  is  the  angle  made  by 
the  line  of  departure  with  the  horizontal. 

The  Angle  of  Elevation,  $',  is  the  angle  between  the  line  of  sight 
and  the  axis  of  the  piece  when  the  gun  is  aimed. 

The  Jump  is  the  angle  j  through  which  the  axis  of  the  piece 
moves  while  the  projectile  is  passing  through  the  bore.  The 
movement  of  the  axis  is  due  to  the  elasticity  of  the  parts  of  the 
carriage,  to  the  play  in  the  trunnion  beds  and  between  parts  of  the 
carriage,  and  in  some  cases  to  the  action  of  the  elevating  device  as 
the  gun  recoils.  The  jump  must  be  determined  by  experiment 
for  the  individual  piece  in  its  particular  mounting.  It  usually 
increases  the  angle  of  elevation  so  that  the  angle  of  departure  is 
greater  than  that  angle. 

The  Point  of  Fall,  f,  or  Point  of  Impact,  is  the  point  at  which 
the  projectile  strikes. 

The  Angle  of  Fall,  aj,  is  the  angle  made  by  the  tangent  to  the 
trajectory  with  the  line  of  sight  at  the  point  of  fall. 

The  Striking  Angle,  a/,  is  the  angle  made  b}^  the  tangent  to  the 
trajectory  with  the  horizontal  at  the  point  of  fall. 

Initial  Velocity  is  the  velocity  of  the  projectile  at  the  muzzle. 

Remaining  Velocity  is  the  velocity  of  the  projectile  at  any  point 
of  the  trajectory. 

Drift,  kf,  is  the  departure  of  the  projectile  from  the  plane  of 
fire,  due  to  the  resistance  of  the  air  and  the  rotation  of  the  pro- 
jectile. 

Direct  Fire  is  with  high  velocities,  and  angles  of  elevation  not 
exceeding  20  degrees. 

Curved  Fire  is  with  low  velocities,  and  angles  of  elevation  not 
exceeding  30  degrees. 

High  Angle  Fire  is  with  angles  of  elevation  exceeding  30 
degrees. 

206.  The  Motion  of  an  Oblong  Projectile. — The  projectile 
as  it  issues  from  the  muzzle  of  the  gun  has  impressed  upon  it  a 
motion  of  translation  and  a  motion  of  rotation  about  its  longer 


EXTERIOR  BALLISTICS.  359 

axis.  The  guns  of  our  service  are  rifled  with  a  right  handed  twist, 
and  the  rotation  of  the  projectile  is  therefore  from  left  to  right 
when  regarded  from  the  rear.  After  leaving  the  piece  the  pro- 
jectile is  a  free  body  acted  upon  by  two  extraneous  forces,  gravity 
and  the  resistance  of  the  air. 

When  the  projectile  first  issues  from  the  piece,  its  longer  axis 
is  tangent  to  the  trajectory.  The  resistance  of  the  air  acts  along 
this  tangent,  and  is  at  first  directly  opposed  to  the  motion  of 
translation  of  the  projectile. 

The  longer  axis  of  the  projectile  being  a  stable  axis  of  rotation 
tends  to  remain  parallel  to  itself  during  the  passage  of  the  pro- 
jectile through  the  air,  but  the  tangent  to  the  trajectory  changes 
its  inclination,  owing  to  the  action  of  gravity.  The  resistance  of 
the  air  acting  always  in  the  direction  of  the  tangent,  thus  becomes 
inclined  to  the  longer  axis  of  the  projectile,  and  in  modem  pro- 
jectiles its  resultant  intersects  the  longer  axis  at  a  point  in  front 
of  the  center  of  gravity. 

In  Fig.  157,  G  being  the  center  of  gravity,  and  R  the  resultant 


FIG.  157. 

resistance  of  the  air,  this  resultant  acts  with  a  lever  arm  I,  and 
tends  to  rotate  the  projectile  about  a  shorter  axis  through  G  per- 
pendicular to  the  plane  of  fire. 

The  resultant  effect  of  the  resistance  of  the  air  on  the  rotating 
projectile  is  a  precessional  movement  of  the  point  of  the  projectile 
to  the  right  of  the  plane  of  fire.  After  the  initial  displacement  of 
the  point  to  the  right  the  direction  of  the  resultant  resistance 
-changes  slightly  to  the  left  with  respect  to  the  axis  of  the  pro- 
jectile, and  produces  a  corresponding  change  in  the  direction  of  the 
precession,  which  diverts  the  point  of  the  projectile  slightly  down- 
ward. 

If  the  flight  of  the  projectile  were  continued  long  enough 
the  point  would  describe  a  curve  around  the  tangent  to  the 


360  ORDNANCE  AND  GUNNERY. 

trajectory;  but  actually  the  flight  of  the  projectile  is  never 
long  enough  to  permit  more  than  a  small  part  of  this  motion 
to  occur. 

The  precession  of  the  point  is  greater  as  the  initial  energy  of 
rotation  is  less.  It  is  therefore  necessary  to  give  to  the  projectile 
sufficient  energy  of  rotation  to  make  the  divergence  of  the  point 
small.  Otherwise  the  precessional  effect  may  be  sufficient  to  cause 
the  projectile  to  tumble. 

When  the  point  of  the  projectile  leaves  the  plane  of  fire  the 
side  of  the  projectile  is  presented  obliquely  to  the  action  of  the 
resistance  of  the  air,  and  a  pressure  is  produced  by  which  the  pro- 
jectile is  forced  bodily  to  the  right  out  of  the  plane  of  fire.  It 
is  to  this  movement  that  the  greater  part  of  the  deviation  of 
the  projectile  is  due. 

DRIFT. — The  departure  of  the  projectile  from  the  plane  of 
fire,  due  to  the  causes  above  considered,  is  called  drift. 

207.  Form  of  Trajectory. — It  may  be  shown  analytically  that 
the  drift  of  the  projectile  increases  more  rapidly  than  the  range. 
The  trajectory  is  therefore  a  curve  of  double  curvature,  convex 
to  the  plane  of  fire. 

The  trajectory  ordinarily  considered  is  the  projection  of  the 
actual  curve  upon  the  vertical  plane  of  fire.  This  projection  so 
nearly  agrees  with  the  actual  trajectory  that  the  results  obtained 
are  practically  correct;  and  the  advantage  of  considering  it, 
instead  of  the  actual  curve,  is  that  we  need  consider  only  that 
component  of  the  resistance  of  the  air  which  acts  along  the  longer 
axis  of  the  projectile  and  which  is  directly  opposed  to  the  motion 
of  translation. 

Determination  of  the  Resistance  of  the  Air. — The  relation 
between  the  velocity  of  a  projectile  and  the  resistance  opposed 
to  its  motion  by  the  air  has  been  the  subject  of  numerous  experi- 
ments. 

In  the  usual  method  of  determining  this  relation  the  velocity 
of  the  projectile  is  measured  at  two  points  in  the  trajectory. 
The  points  are  selected  at  such  a  distance  apart  that  the  path 
of  the  projectile  between  them  may  be  considered  a  right  line, 
and  the  action  of  gravity  may  be  neglected.  The  resistance  of 
the  air  is  then  regarded  as  the  only  force  acting  to  retard  the 


EXTERIOR  BALLISTICS  301 

projectile,  and  is  considered  as  constant  over  the  path  between 
the  two  points. 

The  loss  of  energy  in  the  projectile,  due  to  the  loss  of  velocity, 
is  the  measure  of  the  effect  of  the  resistance  of  the  air,  and  is 
equal  to  the  product  of  the  resistance  into  the  path.  The  resist- 
ance thus  obtained  is  the  mean  resistance,  and  corresponds  to 
the  mean  of  the  two  measured  velocities. 

EARLY  EXPERIMENTS. — The  first  experiments  were  those  of 
Robins  in  1742.  For  the  measurement  of  velocities  he  used  the 
ballistic  pendulum.  His  conclusions  were,  that  up  to  a  velocity 
of  1100  foot  seconds  the  resistance  is  proportional  to  the  square 
of  the  velocity;  beyond  1100  f.  s.  the  resistance  is  nearly  three 
times  as  great  as  if  calculated  by  the  law  of  the  lower  velocities. 

Hutton  in  1790,  with  the  improved  ballistic  pendulum,  made 
numerous  experiments  with  large  projectiles.  His  conclusions 
were  that  the  resistance  increases  more  rapidly  than  the  square 
of  the  velocity  for  low  velocities,  and  for  higher  velocities  that 
it  varies  nearly  as  the  square. 

General  Didion  made  a  series  of  experiments  at  Metz  in  1840 
with  spherical  projectiles  of  vaiying  weights.  His  conclusions 
were  that  the  resistance  varied  as  an  expression  of  the  general 
form  a(v2  +  bv3},  a  and  b  being  constants.  This  formula  held  for 
low  velocities  only. 

Experiments  were  again  made  at  Metz  in  1857.  Electro-ballis- 
tic instruments  were  now  used  for  the  measurement  of  velocities. 
The  conclusions  from  these  experiments  were  that  the  resistance 
varies  as  the  cube  of  the  velocity.  Experiments  by  Prof.  Helie 
at  Gavre  in  1861  gave  practically  the  same  results. 

The  experiments  above  described  were  made  principally  with 
spherical  projectiles.  The  difference  in  the  nature  of  the  resistance 
experienced  by  oblong  and  spherical  projectiles,  together  with  the 
difference  in  the  velocities,  then  and  later,  may  account  for  the 
wide  difference  in  the  results  obtained  from  these  and  from  later 
experiments. 

LATER  EXPERIMENTS. — The  Rev.  Francis  Bashforth  made 
exhaustive  experiments  in  England,  in  1865  and  again  in  1880, 
using  comparatively  modern  projectiles  and  accurate  ballistic 
instruments.  His  conclusions  were,  that  for  velocities  between 


3€2  ORDNANCE  AND  GUNNERY. 

900  and  1100  f.  s.  the  resistance  varied  as  the  sixth  power  of 
the  velocity;  between  1100  and  1350  f.  s.,  as  the  cube  of  the 
velocity;  and  above  1350  f.  s.,  as  the  square  of  the  velocity. 

The  most  recent  experiments  are  those  made  by  Krupp  in 
1881  with  modem  guns,  projectiles,  and  velocities.  The  results  of 
these  experiments  were  used  by  General  Mayevski  in  the  deduc- 
tion of  the  formulas  for  the  resistance  of  the  air  which  are  now 
generally  used. 

CONCLUSIONS  FROM  THE  EXPERIMENTS. — The  experiments  have 
shown  that  the  resistance  of  the  air  varies  with  the  form  of  the 
projectile,  with  its  area  of  cross  section,  with  the  velocity  of  the 
projectile,  and  with  the  density  of  the  air.  Considering  the  form 
of  the  projectile  the  resistance  is  affected  principally  by  the  shape 
of  the  head,  and  by  the  configuration  at  the  junction  of  the  head 
and  body.  The  ogival  head  encounters  less  resistance  than  any 
other  form  of  head.  The  resistance  was  found  to  increase  directly 
with  the  area  of  cross  section  of  the  projectile,  and  directly  with 
the  density  of  the  air. 

208.  Mayevski's  Formulas  for  Resistance  of  the  Air. — In 
expressing  the  relation  between  the  resistance  of  the  air  and  the 
velocity  of  the  projectile,  General  Mayevski  placed  the  retarda- 
tion, as  determined  in  Krupp's  experiments,  equal  to  an  expres- 
sion which  involves,  together  with  an  unknown  power  of  the 
velocity,  quantities  whose  values  are  dependent  on  the  weight, 
form,  and  cross  section  of  the  projectile,  and  on  the  density  of 
the  air. 

Calling  p  the  resistance  of  the  air, 

w  the  weight  of  the  projectile  in  pounds, 
g  the  acceleration  of  gravity, 
the  retardation  is  pg/w 

Representing  by  R  the  retardation  of  the  projectile,  make 

in  which  A  is  a  constant  and  n  some  power  of  the  velocity,  both 
to  be  determined  from  the  experiments. 

THE  BALLISTIC  COEFFICIENT,  C.— The  quantity  C  hi  the  equa- 
tion was  given  a  value 

o  cd2 


EXTERIOR  BALLISTICS. 


363 


in  which  $i  is  the  standard  density  of  the  air, 

d  the  density  at  the  time  of  the  experiment, 
c   the  coefficient  of  form, 
d  the  diameter  of  the  projectile  in  inches, 
w  the  weight  of  the  projectile  in  pounds. 

By  the  introduction  of  this  coefficient  into  the  value  of  the  retarda- 
tion, the  effect  of  variations  in  weight,  form,  and  cross  section 
of  the  projectile,  and  in  the  density  of  the  air,  may  be  considered. 

The  coefficient  of  form  c  was  taken  as  unity  for  the  standard 
projectiles.  For  projectiles  of  a  form  that  offers  greater  resistance 
the  value  of  c  will  be  greater  than  unity.  Examination  of  equa- 
tion (1)  shows  that  as  c  increases,  and  C  decreases,  the  retardation 
is  increased;  a  result  also  obtained  by  increase  in  d  or  d,  that  is 
in  the  cross  section  of  the  projectile  or  in  the  density  of  the  air; 
while  by  an  increase  in  w,  C  is  increased  and  the  retardation  is 
diminished.  The  coefficient  C  is  therefore  the  measure  of  the  bal- 
listic efficiency  of  the  projectile. 

The  value  of  c  for  all  projectiles  in  our  service  is  usually  taken 
as  unity. 

The  density  of  the  air  is  a  function  of  the  temperature  and 
of  the  atmospheric  pressure.  The  values  of  di/d  for  different 
atmospheric  pressures  and  temperatures  are  found  in  Table  VI 
of  the  ballistic  tables. 

Mayevski  determined,  from  Krupp's  experiments,  values  for  n 
and  A  for  different  velocities  as  follows. 


Velocities,  f.  s. 

n 

log  A 

Velocities,  f.  s. 

n 

log  A 

Above    2600 

1.55 

3.6090480 

1230  to  970 

5 

14.8018712 

2600  to  1800 

1.7 

3.0951978 

970  to  790 

3 

8.7734430 

1800  to  1370 

2 

4.1192596 

Below  790 

2 

5.6698914 

1370  to  1230 

3 

8.9809023 

209.  Trajectory  in  Air.  Ballistic  Formulas. — In  the  deduc- 
tion of  the  ballistic  formulas  the  trajectory  is  considered  as  a 
plane  curve.  The  line  of  sight  is  taken  as  horizontal.  The  angle 
of  elevation  is  taken  as  the  angle  of  departure,  and  the  striking 
angle  becomes  the  angle  of  fall. 

The  trajectory  so  considered  is  called  The  Horizontal  Trajec- 
tory. 


364 


ORDXAXCE  AND  GUNNERY. 


Considering   the   motion    of    translation    only,    and   that   the 
resistance  of  the  air  is  directly  opposed  to  this  motion,  let,  Fig.  158, 


R  be  the  retardation  due  to  the  resistance  of  the  air,  its 

value  being  given  by  equation  (1); 
V,  the  initial  velocity; 

v,  the  velocity  at  any  point  of  the  trajectory  whose  co- 
ordinates are  z  and  y; 

Vi,  the  component  of  v  in  the  direction  of  x; 
(j>,  the  angle  made  with  the  horizontal  by  the  tangent  to  the 

trajectory  at  the  origin,  or  the  angle  of  departure; 
6,  the  value  of  <£  for  any  other  point  of  the  trajectory; 
CD,  the  angle  of  fall; 
x  and  y,  the  co-ordinates  of  any  point  of  the  trajectory,  in  feet; 

X,  the  whole  range,  in  feet. 

EQUATIONS  OF  MOTION. — The  only  forces  acting  on  the  pro- 
jectile after  it  leaves  the  piece  are  the  resistance  of  the  air  and 
gravity. 

The  resistance  of  the  air  is  directly  opposed  to  the  motion  of  the 
projectile,  and  continually  retards  it.  Gravity  retards  the  pro- 
jectile in  the  ascending  portion  of  the  trajectory,  while  it  acceler- 
ates it  in  the  descending  portion. 

Considering  the  ascending  portion  of  the  trajectory,  the  velocity 
in  the  direction  of  a:  is 


v  cos  6  =  vi=  dx/dt  dx  =  v\dt 

The  velocity  in  the  direction  of  y  is 

v  sin  6  =  Vi  tan  6  =  dy/dt       dy  =  v\  tan  6  dt 
The  retardation  in  the  direction  of  y  is  therefore 
-d(vi  tan  d)/dt  =  g  +  Rsm  6 


(2) 


(3) 


(4) 


EXTERIOR  BALLISTICS.  365 

Since  gravity  has  no  component  in  a  horizontal  direction,  the 
retardation  in  the  direction  of  x  is 

-  dvi  /dt  =  Rcosd  dt=-  dvi  /R  cos  6  (5) 

Substituting  this  value  of  dt  in  (2),  (3),  and  (4),  and  performing 

the  differentiation  indicated  in   (4),  d  tan  6  being  dd/cos2d,  we 
obtain 

dx  =  —  Vidvi  /R  cos  6  (6) 


dy=  —  Vi  tan  6  dv\/R  cos  6  (7) 

dd  =  g  cos  6  dvr  /Rvi  (8) 


The  four  equations  (5)  to  (8)  are  the  differential  equations  of 
motion  of  the  projectile,  and  if  they  could  be  integrated  directly 
they  would  give  the  values  of  t,  x,  y,  and  6  for  any  point  of  the 
trajectory.  But  as  they  are  expressed  in  terms  of  R,  v,  and  6, 
three  independent  variables,  the  direct  integration  is  impossible. 

The  value  of  R  is  given  by  Mayevski's  formulas,  R  =  Avn/C, 
n  representing  the  exponent  of  v  for  any  particular  velocity.  Sub- 
stituting this  value  of  R  in  (6),  the  equation  may,  by  means  of 
the  relation  v  cos  Q  =  VI,  be  put  in  the  form 

dx=-Ccosn-lddv1/Av1n-1  (9) 

The  second  member  would  be  an  exact  integral  were  it  not 
for  the  factor  cosn~ld.  In  direct  fire  cos  6  differs  but  little  from 
unity,  and  it  might  be  taken  as  unity  without  appreciable  error. 
cos""1/?  would  then  be  unity  and  the  expression  would  be  integrable. 
A  closer  approximation,  however,  as  shown  by  Siacci,  results 

from  making 

cosn~  16  =  cosn~2<f> 

Making  this  substitution  equation  (9)  may  be  brought  by 
reduction,  see  foot  note,  to  the  form 

dx  __  C 


A  (V!  sec 

cosn-2<£=l/secn-2«£  =  s 
is  constant,  therefore  sec  <£dVi  =  d(v,  sec  6). 


ORDNANCE  AND  GUNNERY. 

Vi  sec  fi  =  v  cos  0/cos  <j>  =  u 
V i  sec  (j>  =  V  cos  0/cos  $  =  V 

Making  these  substitutions   in  equation  (10)  and   integrating 
between  the  limits  u  and  V  we  obtain 


x  — 


I. 


-i-     JL/I 

tn-2  yn-2j 


(11) 


And  similarly  equations  (5)  and  (8)  may  be  brought  to  the  forms 

1  1 


t_ 


(n-l)A  cos 


tan  $—  tan  ^=  —       "T-F 

nA  cos2  (f)Lu 


—  T/^ 
n       VnJ 


(12) 
(13) 


210.  To  simplify  equations  (11)  to  (13),  make 

s,u}_  1  ,    c 

'     (n  —  2)Aun~2 

1 


(14) 


nAu- 

The  reason  for  the  addition  of  the  constants  will  appear. 
Making  these  substitutions,  equations  (11)  to  (13)  become 

x  =  C\S(u)-S(V}\  (15) 


cos 


tan  ^  = 


C 


Making  in  the  last  equation  tan  6  —  dy/dx,  and  making 


(16) 

(17) 

(140 


EXTERIOR  BALLISTICS.  367 

equation  (17)  may  be  brought  to  form,  see  foot  note, 


Equations  (15)  to  (18),  with  the  equations 

cos  d 

and 

18l    w 


are  the  fundamental  equations  of  Exterior  Ballistics,  and  con- 
stitute the  method  of  Siacci,  an  eminent  Italian  ballistician.  The 
essence  of  the  method  lies  in  the  use  of  u,  called  by  Siacci  the 
pseudo  velocity,  for  v,  the  actual  velocity. 

In  all  problems  of  direct  fire,  since  the  difference  between  <£ 
and  6  is  not  great,  u  may  be  used  for  v  with  sufficient  accuracy. 
In  problems  in  curved  and  high  angle  fire,  and  in  direct  fire  when 
greater  accuracy  is  desired,  we  pass  from  the  value  of  u  to  the 
value  of  v  by  means  of  equation  (19).  It  will  be  seen  from  this 
equation  that,  since  u  cos  <f>  =  v  cos  6,  u  is  the  component  of  v 
parallel  to  the  line  of  departure. 

The  Ballistic  Coefficient.  —  The  ballistic  coefficient,  like  the 
force  coefficient  in  the  interior  ballistic  formulas,  affords  a  con- 
venient means  of  introducing  into  the  exterior  ballistic  formulas 
any  correction  necessary  to  make  the  formulas  applicable  to  con- 
ditions differing  from  the  conditions  for  which  the  formulas  were 
deduced. 

From  (17), 

<ty=tan  4>dx-  —  ^-r{I(u)dx-I(V)dx\)  v  (17a) 

—  COS     <p 

From  (10),  and  vt  sec  <j>  =  u,  dx=Cdu/Au*~l 

Substitute  this  value  in  the  second  term  of  the  second  member  of  (17a). 
Integrate  the  equation  between  the  limits  u  and  V  with  the  help  of  (14').  and 
divide  through  by  x. 


x  ^  cos 

Substitute  for  C/x  its  value  from  (15). 


368  ORDNANCE  AND  GUNNERY. 

For  general  use  with  the  formulas  of  exterior  ballistics 
Mayevski's  value  for  C,  page  362,  is  changed  by  the  introduction 
of  two  quantities,  /  and  p,  so  that  the  value  of  the  ballistic 
coefficient  takes  the  form  written  in  equation  (20). 

/  is  called  the  altitude  factor,  and  brings  into  consideration  the 
diminution  in  the  density  of  the  air  as  the  altitude  of  the  tra- 
jectory increases.  The  value  of  /  is  greater  than  unity  and  de- 
pends upon  the  mean  altitude  of  the  trajectory,  which  is  taken 
as  two-thirds  of  the  maximum  altitude. 

/?  is  an  integrating  factor,  and  corrects  for  the  error  due  to  cer- 
tain assumptions  made  in  deducing  the  primary  equations,  when 
these  equations  are  applied  to  a  trajectory  whose  curvature  is 
considerable.  /?  is  approximately  unity  in  all  problems  of  direct 
fire.  The  product  /?c  is  called  the  coefficient  of  reduction. 

When  in  the  statements  of  ballistic  problems  the  data  required 
to  determine  §i/d,  ft  or  c  is  not  given,  the  value  unity  is  assumed 
for  the  factor,  f  is  also  assumed  as  unity  unless  a  correction  for 
altitude  is  desired.  When  all  these  factors  are  unity  the  ballistic 
coefficient  becomes 


211.  The  Functions.  —  The  functional  expressions  inequations 
(15)  to  (18)  are  called:  S(u)  the  space  function,  T(u)  the  time 
function,  I(u)  the  inclination  function,  and  A(u)  the  altitude 
function.  Their  values  are  given  by  the  equations  (14)  and  (14'). 
The  values  of  these  functions  for  values  of  u  from  3600  to  100 
foot  seconds  have  been  calculated,  and  form  Table  I  of  the  Bal- 
listic Tables. 

Since  V  is  a  particular  value  of  u  the  values  of  the  functions 
of  V  are  included  in  the  table  as  values  of  the  functions  of  u. 
For  example,  to  find  the  value  of  S(V),  V  being  given,  enter 
the  table  with  the  value  of  V  as  a  value  of  u  and  take  out  the 
corresponding  value  of  S(u). 

The  quantities  Q,  Q',  and  Q",  in  the  values  of  the  functions, 
equations  (14),  are  arbitrary  constants;  and  the  purpose  of  includ- 
ing them  is  to  provide  a  means  for  avoiding  abrupt  changes  in 
the  tables  at  those  points  where  in  Mayevski's  formulas  the  values 
of  A  and  n  change. 


EXTERIOR  BALLISTICS.  369 

CALCULATION  OF  THE  FUNCTIONS.  —  The  method  of  employing 
the  constants  in  forming  the  tables  is  best  shown  by  an  example. 
The  value  of  the  S  function  is,  equation  (14), 


For  va'ues  of  v  greater  than  2600  f.  s.,  we  have  from  May- 
evski's  formulas,  n  =  1.55.  Therefore  for  a  velocity  greater  than 
2600  f  .  s. 


In  order  to  avoid  the  use  of  large  numbers  Table  I  of  the  lat- 
est ballistic  tables,  published  in  1900,  is  so  constructed  that  the 
S,  A,  and  T  functions  reduce  to  zero  for  i/  =  3600.  I(u)  reduces 
to-  zero  for  u=  <x>.  We  have  then  for  S(u),  when  w  =  3600 


0.45 


and  therefore 

^- 

For  any  other  value  of  u  down  to  2600 


=  —— 
0.45^! 

For  velocities  between  2600  and  1800  f.  s.,  n  =  1.7,  and 

««>— 


(21) 


Q2  must  have  such  a  value  as  to  make  the  value  of  S(u)  for 
w  =  2600  the  same  as  the  value  determined  from  equation  (21) 
with  this  value  of  u.  Therefore 


-0.3  0.45 


-(2600 


from  which  the  value  of  Q2  can  be  determined. 

The  same  process  is  followed  at  each  change  in  the  values  of 
n  and  A. 


370  ORDNANCE  AND  GUNNERY. 

When  n  =  2  equation  (11)  becomes  indeterminate  and  the 
values  of  the  functions  cannot  be  determined  as  above;  but 
making  n  =  2  in  equation  (10)  and  integrating  we  obtain 

C 

X==~~A 

S(u)  becomes  in  this  case 


_ 

INTERPOLATION  IN  TABLE  I.  —  This  is  effected  by  the  ordinary 
rules  of  proportional  parts.  The  difference  between  successive 
values  of  u  varies  from  unity  in  one  part  of  the  table  to  2,  5,  and 
10  in  other  parts.  This  difference  must  be  carefully  noted  in 
interpolating. 

212.  Formulas  for  the  Whole  Range.  —  Designate  the  whole 
range,  Fig.  158,  by  X,  the  corresponding  time  of  flight  by  T,  the 
angle  of  fall  (considered  positive  for  convenience)  by  a>,  and  use  the 
subscript  u  to  designate  the  values  of  u  and  v  at  the  point  of 
fall. 

At  the  point  of  fall  y  =  0  and  6=  —  a>;  and  after  combining 
equations  (17)  and  (18)  to  eliminate  I(V)  from  (17),  equations  (15) 
to  (19)  become,  respectively, 

(22) 

(23) 

C  .     A(uJ-A(V) 


(25) 

u<o  =  va  cos  oj/cos  $  (26) 

At  the  summit  of  the  trajectory  0  =  0.     Using  the  subscript  0 
to  designate  the  summit,  equations  (17)  and  (19)  become,  after 

reduction, 

(27; 


u0  =  v0/cos  (f)  (28) 


EXTERIOR  BALLISTICS.  371 

Combining  (27)  and  (25)  we  have 

A(uJ-A(V) 
I(Uo)=S(uJ^S(V) 
Therefore  (24)  and  (25)  become 

(30) 
(31) 

213.  The  Ballistic  Elements.— The  quantities  C,  u,  V,  <f>, 
6,  aj,  T,  and  X  in  the  previous  equations  are  called  the  ballistic 
elements.  When  referring  to  the  end  of  the  range  they  are 
written  as  capitals,  or  with  the  subscript  tt.  For  any  other  point 
of  the  trajectory  they  are  written  as  small  letters,  with  suitable 
subscript  if  desired.  The  subscript  0  always  refers  to  the  summit 
of  the  trajectory.  The  equations,  by  reason  of  Siacci's  assump- 
tion for  the  value  of  cosn~  10,  express  the  relations  existing  between 
these  elements  in  direct  fire  only. 

When  three  or  more  of  the  elements  are  given  the  others  may 
be  determined. 

The  Rigidity  of  the  Trajectory. — According  to  the  principle 
of  the  rigidity  of  the  trajectory,  which  is  mathematically  demon- 
strated, the  relations  existing  between  the  trajectory  and  the 
chord  representing  the  range  are  sensibly  the  same  whether  the 
chord  be  horizontal  or  inclined  to  the  horizon,  provided  that  the 
quadrant  angle  of  departure  and  the  angle  of  position  are  small 
or  that  the  difference  between  them  is  small.  That  is  to  say 
that,  considering  $+£  and  e  as  small,  in  Fig.  156,  if  the  trajec- 
tory bdf  and  its  chord  bf  were  revolved  about  the  point  6  until  bf 
were  horizontal,  the  relation  of  the  trajectory  to  bf  would  not 
change.  A  trajectory  calculated  for  a  horizontal  range  equal  to  bf 
would  then  answer  as  the  trajectory  for  the  actual  inclined  range  bf. 
Therefore  when  the  quadrant  angle  of  departure,  <£+e,  is 
small  we  may  consider  bf,  or  any  other  chord  of  the  trajectory, 
as  a  horizontal  range;  and  we  may  apply  to  the  trajectory  sub- 
tended by  the  chord  the  formulas  deduced  for  a  horizontal  range. 
If  however  the  quadrant  angle  of  departure  is  large,  the  prin- 


372  ORDNANCE  AND  GUNNERY. 

ciple  of  the  rigidity  of  the  trajectory  applies  only  when  the  angle 
of  position  is  also  large,  that  is  when  <£+e  does  not  differ  much 
from  £.  Therefore  in  any  complete  high  angle  trajectory  for  a 
horizontal  range  the  principle  of  the  rigidity  of  the  trajectory 
applies  only  to  a  part  of  the  trajectory  near  the  origin.  This 
part  may  be  treated  as  a  horizontal  range  whose  angle  of  departure 
is  the  difference  between  the  quadrant  angle  of  departure  of  the 
horizontal  trajectory  and  the  angle  of  position. 

When  the  difference  between  (j>+$  and  e  is  small,  </>  must 
be  small.  It  is  therefore  evident  that,  in  direct  fire,  the  principle 
of  the  rigidity  of  the  trajectory  applies  whenever  the  angle  of 
departure  is  small. 

This  principle  enables  us  to  use  the  elements  calculated  for  a 
horizontal  range  when  firing  at  objects  situated  above  or  below 
the  level  of  the  gun. 

214.  Use  of  the  Formulas.  —  The  method  of  using  the  formulas 
may  best  be  shown  by  considering  a  problem. 

Problem  i.  —  What  is  the  time  of  flight  of  a  3-inch  projectile 
weighing  15  Ibs.,  for  a  range  of  2000  yards;  muzzle  velocity,  1700 
f.  s.? 

The  given  data  are  C  =  15/9,  F  =  1700,  and  Z  =  6000,  the 
range  being  always  taken  in  feet.  T  is  required. 

These  formulas  apply: 

(23) 


(25) 

X  =  C\S(uJ-S(V)\  (22) 

Take  the  T,  S,  A,  and  /  functions  of  V  from  Table  I. 

Determine  S(uJ  from  (22). 

Find  uu  from  Table  I,  and  take  from  the  Table  T(uJ  and 
A(uJ. 

Find  <£  from  (25). 

Find  T,  required,  from  (23).  Ans.  7  =  4.48  seconds. 

215.  Secondary  Functions.  —  The  most  important  problems  in 
gunnery  may  be  solved  by  means  of  equations  (22)  to  (31)  and 


EXTERIOR  BALLISTICS.  373 

ballistic  Table  I,  but  some  of  the  solutions  are  indirect  and  ten- 
tative and  therefore  very  laborious.  The  processes  of  solution 
have  been  greatly  abbreviated  and  the  labor  greatly  reduced 
by  the  introduction  of  secondary  functions,  whose  values,  for  all 
the  requirements  of  modern  gunnery,  have  been  calculated  and 
collected  in  Table  II  of  the  ballistic  tables. 

The  development  of  the  science  of  exterior  ballistics  to  its 
present  accuracy  and  comparative  simplicity  is  principally  due 
to  Colonel  James  M.  Ingalls,  U.  S.  Army,  whose  interior  ballistics 
are  set  forth  in  Chapter  III. 

From  equation  (15)  we  have 


and  substituting  the  values  of  S(u)  and  S(V),  see  (14), 

1  x_  I 

(n-2)Aun~2  ~  C  +  (n-2)AV"-2 

From  this  equation  it  is  apparent  that  the  value  of  the  pseudo 
velocity  u,  at  any  point,  is  a  function  of  x/C  and  V  only,  and  is 
independent  of  the  height  of  the  point  in  the  trajectory. 

Make 

z  =  x/C  Z  =  X/C 

It  will  be  seen  hi  equations  (16),  (17),  and  (18)  that  t,  6,  and  y 
are  functions  of  u  and  therefore  also  functions  of  z  and  of  V. 

The  secondary  functions,  whose  values  are  here  given,  are  all 
functions  of  Z  and  V,  and  are  tabulated  with  Z  and  V  as  arguments. 

A(u)-A(V)     Tf^ 
A  ~S(u)-S(V) 


A(u)-A(V) 
~S(u)-S(V) 


(32) 


T'  =  T(u}-T(V) 
B'  =  B/A 

The  subscripts  are  dropped  in  these  expressions  since  they 
only  serve  to  indicate  particular  values  of  u,  while  the  table 
contains  the  values  of  A,  B,  etc.,  for  all  the  values  of  u. 


374  ORDNANCE  AND  GUNNERY. 

The  table  also  contains,  in  the  column  u,  the  values  of  u  for 
all  values  of  Z  and  V. 

Equations  (23),  (24),  and  (25)  may  now  be  put,  by  reduction, 
into  the  following  exceedingly  simple  forms. 

T  =  CT'/cos<j>  (33) 

sin  2  <£  =  AC  (34) 

tan  a)  =  BC/2  cos2  0  =  5'  tan  <f>  (35) 

Equations  (17)  and  (18)  may  also  be  put  in  the  forms 

tan  0=^(4  -a')  (36) 

*(A-«)  (37) 

In  these  equations  a  and  a'  are  the  values  of  A  and  A'  corre- 
sponding to  z  =  x/C  for  the  particular  point  of  the  trajectory  con- 
sidered, while  A  and  A'  are  the  values  corresponding  to  Z  =  X/C 
for  the  whole  range. 

216.  At  the  summit  tan  6  reduces  to  zero;  and  we  obtain  from 
equation  (36),  writing  oV  for  a'  at  the  summit, 

a0'  =  A  (38) 

Equation  (37)  then  becomes 

».-5(«.'-a«)  (38') 


From  the  third  equation  (32)  we  have  for  the  summit 
bo  =  a0f  —  ao.  With  this  relation  and  the  relation  z0  =  Xo/C,  and 
making 


equation  (38')  reduces  to  the  form 

(39) 


yo  representing  the  maximum  ordinate. 

To  obtain  a0"  for  use  in  this  equation  we  find  in  Table  II, 
in  the  A'  column,  the  value  of  A  as  determined  for  the  whole 


EXTERIOR  BALLISTICS.  375 

range.    With  this  value  as  A'  and  the  given  value  of  V  we  find 
a0",in  the  A"  column. 

Write  Z=X/C  (40) 

v  =  ucos<j>/cosd  (41) 


and 

f  [3.79239]  C2£'/cos3  <f>  (seacoast  guns) 

Drift  (yds.)  =  J    _  (43) 

[  [3.92428]  C2I>'/cos3  <£  (field  guns) 

which  is  Mayevski's  formula  for  drift,  abbreviated  for  tabulation 
by  Colonel  Ingalls.  The  values  of  D'  are  found  in  Table  II. 

We  have  in  the  equations  (33)  to  (43)  the  principal  formulas 
required  for  the  solution  of  nearly  all  the  problems  of  direct  fire. 

While  the  formulas  apply  strictly  to  direct  fire  only,  where  the 
values  of  <£  and  6  are  such  as  to  permit  the  use  of  Siacci's  value 
of  cosn-1^  without  appreciable  error,  they  give  sufficiently  accu- 
rate results  for  curved  fire,  and  they  are  used  for  curved  fire  as 
well. 

They  are  made  applicable  to  high  angle  fire  by  giving  to  the 
coefficient  c  in  the  ballistic  coefficient  such  values  as  will  make  the 
results  obtained  from  the  formulas  agree  with  the  results  obtained 
in  actual  firings.  For  the  low  velocities  used  in  mortars  and 
howitzers  the  formulas  are  simplified,  as  will  later  be  shown. 

Ballistic  Tables.  —  The  Ballistic  Tables,  which  are  issued  by 
the  War  Department,  consist  of  three  volumes,  entitled:  Ar- 
tillery Circular  M,  Series  of  1893  (printed  in  1900),  Supplement  to 
Artillery  Circular  M  (1903),  and  Supplement  No.  2  to  Artillery  Cir- 
cular M  (1904).  The  supplements  extend  Tables  II,  IV,  and  V  of 
Artillery  Circular  M. 

In  addition  there  has  appeared  a  simplification  of  Table  IV  in 
the  Journal  of  the  United  States  Artillery,  number  for  January  and 
February,  1905. 

Artillery  Notes,  No.  ®5,  issued  by  the  War  Department,  1905, 
contains  a  corrected  table  to  replace  Table  VI  of  Artillery  Circular 
M,  the  latter  table  having  been  found  to  be  based  on  incorrect  data. 

The  ballistic  formulas  are  found  assembled  on  page  VIII  of  the 


376  ORDNANCE  AND  GUXNERY. 

first  book  of  tables,  Artillery  Circular  M,  so  that  the  books  of 
tables  contain  all  that  is  needed  for  the  solution  of  most  of  the 
problems  of  gunnery. 

Under  the  heading  Formulas  to  be  used  with  Table  II,  on  page 
VIII  of  Artillery  Circular  M,  appears  the  formula 

S(u)=Z+S(v) 
which  is  another  form  of 

X  =  C{S(u)-S(V)} 

This  formula,  which  is  sometimes  convenient  to  use,  requires  the 
use  of  Table  I. 

To  understand  the  additional  formulas  under  this  heading  on 
page  VIII  of  the  ballistic  tables  it  is  only  necessary  to  know  that 
£  represents  the  angle  of  position  of  a  target,  not  on  the  same  level 
with  the  gun,  whose  horizontal  distance  from  the  gun  is  x,  and 
that  0Z  is  the  angle  of  departure  for  the  horizontal  range  x.  a  is 
the  particular  value  of  A  that  corresponds  to  the  value  of  x. 

These  formulas  express  the  relations  that  exist  between  (f>,  e, 
and  <}>x.  They  are  used  to  determine  the  quadrant  angle  of  elevation 
for  a  target  situated  so  much  above  or  below  the  level  of  the  gun 
and  at  such  a  range  that  the  principle  of  the  rigidity  of  the  trajectory 
cannot  be  applied. 

EXTERIOR   BALLISTIC   FORMULAS. 

The  formulas  required  in  the  solutions  of  most  ballistic  prob- 
lems are  here  assembled  for  convenience.  There  are  included  the 
formulas  already  deduced  and  others  which  are  deduced  later. 

DIRECT   FIRE. 
F>825f.  s.     <£<20° 

C  =  /  (42)        Z  =  X/C  (40) 


sin  2  0  =  AC  (34)        T  =  Cr/cos  <£  (33) 

tan  tt»  =  5'  tan  <f>  (35)         v  =  u  cos  <j>/cos  6  (41) 

y  =  x  tan  <f>  (A-  a)  /A  (37)  a0'  =  A  =  sin  2  <f>/C  (38) 

tan  6  =  tan  <j>  (A  -  a'}  /A  (36)  y0  =  a0"  C  tan  0  (39) 


EXTERIOR  BALLISTICS.  377 

CORRECTION   FOR   ALTITUDE. 

log  (log  /)  =  log  7/0+5.01765  (44) 

DANGER  SPACE  AND  DANGER  RANGE. 


(51)        /  =  /0+--(/1-/0)      (53) 
SOT-CI 

AX=X-x  (54)        a0'a0"  =  2  y0/C2  (55) 

DRIFT. 

Seacoast  Guns.     Drift  (yds.)  =  [3.79239]C2Z)'/cos3  <j>  ' 

(4o) 
Field  Guns.  Drift  (yds.)  =  [3.92428]C2D'/cos3  </> 

WIND    EFFECT  —  RANGE. 

JF  =  TFpcos<£  (45)        V'  =  V±JV  (46) 

sin  4<f>  =  Wpsin<f>/V'  (47)         </>'  =  <^<£  (48) 

AX  (ft.)  =X'-  (Xdb  WPT]  (49) 

WIND    EFFECT  —  DEVIATION   FOR  8,    10,    12-INCH   PROJECTILES. 

/         T  (sec  )        \2 
Deviation  (yds.)  =  [7.00000]  sin  «PF(m.p.h.)  (330QO  +  ^  (yds.)j   (50) 

CURVED   FIRE. 

Always  correct  for  altitude. 

For  7>825  f.  s.  and  <£,  20°  to  30°,  use  formulas  for  direct  fire, 
Use  the  following  formulas  when 

7<825f.  s.        <£<30° 

C  =  /||.  '  (42)        Z=X/Q  (40) 

log  (log  /)  =log  y0+  5.01765  (44) 

sin  2  <j>  =  [5.80618]  AC/V2         (56)        tan  a,  =  B'  tan  $  (35) 

»W  =  [3.09691K  cos  ^  ^/cos  °>  (57) 

T  =  [2.90309]  Cr/7  cos  0  (58) 


378  ORDNANCE  AND  GUNNERY. 

HIGH   ANGLE   FIRE. 


Always  correct  for  altitude. 

When  the  coefficient  of  reduction  c  is  known  use  Table  IV. 

When  the  coefficient  of  reduction  is  not  known  use  the  formulas 
for  direct  fire  and  Table  II,  or  Table  'I  in  those  problems  for 
which  Table  II  is  not  sufficiently  extended. 

CURVATURE   OF   EARTH. 

Curvature  (ft.)  =  [7.33289JX2  (yds.)  (59) 

217.  Interpolation  in  Table  II.  —  Exact  formulas  for  inter- 
polation in  Table  II  are  deduced  and  explained  in  the  appendix 
to  this  chapter.  These  formulas  greatly  facilitate  the  solution  of 
ballistic  problems.  A  thorough  understanding  of  the  interpola- 
tion formulas,  and  facility  in  their  use,  should  be  acquired  before 
proceeding  further.  These  formulas,  which  are  here  written,  will 
be  used  in  place  of  the  interpolation  formulas  given  on  page  VIII 
of  the  ballistic  tables,  as  the  latter  formulas  are  approximate  only. 

Double  Interpolation  Formulas  —  Ballistic  Table  II. 

/  =  non-tabular  value  of  any  function  corresponding  to  the  non- 

tabular  values  F  and  Z. 
fo  =  tabular  value  of  function  corresponding  to  tabular  values  VQ 

and  ZQ  always  next  less  than  V  and  Z. 
h  =  difference  between  velocities  given  in  caption  of  table. 
Ji>0  and  Jzo  =  tabular  differences  for  /0. 
Jvi  =  tabular  difference  next  following  4v0  in  same  table. 
/[+zj  indicates  that  function  decreases  as  F  -increases,  and  increases 

•as  Z  increases. 

Use  the  following  formulas  for  the  functions  A,  Af,  B,  T',  log 
C',  .and  Dr  throughout  the  table.  They  also  apply  for  some  values 
of  the  functions  A"  and  log  B'  when  V  >  2500. 

Z-Z0          V-Vp          Z-Z0V-Vo 


EXTERIOR   BALLISTICS.  379 


M/o- 

F7-X100 


Use  the  following  formulas  for  the  functions  A"  and  log  £' 
when  ~F<2500,  and  for  some  values  beyond  that  point. 

V-V0.     ,Z-Z0  V-VQ 


z-z0 

AVQ+  (AV1-  AVQ  ° 


xh 


z=z0+-  v_y  xioo 


Use  the  following  formulas  for  the  function  i 


AvQ-  (Av0- 


Z=Z0+ 


Inspect  the  tables  to  determine  how  the  function  varies  with  V 
and  Z,  and  select  the  proper  group  of  formulas. 


380  ORDNANCE  AND   GUNNERY. 

Exercise  great  care  in  the  use  of  the  plus  and  minus  signs. 

As  the  numbers  in  the  difference  columns  of  the  table  are 
written  as  whole  numbers  we  must,  when  using  the  interpolation 
formulas,  treat  the  tabular  values  of  the  functions  as  whole  num- 
bers, and  afterwards  put  the  decimal  point  where  it  belongs. 

Regarding  the  interpolation  formulas  we  will  note  that  the  pro- 
portional parts  of  the  differences  AzQ  and  Ji>0  are  always  applied 
to  the  tabular  value  of  the  function,  /0,  with  a  sign  indicated  by 
the  manner  of  variation  of  the  function  with  Z  and  V  respectively; 
positive  if  the  function  is  increasing,  negative  for  a  decreasing 
function.  The  sign  of  the  last  term  of  the  /  formulas  is  positive  if 
the  signs  of  the  preceding  terms  are  similar,  and  negative  if  they 
are  dissimilar. 

In  the  formulas  for  V  and  Z  the  fractional  coefficients  of  h  and 

y  _  y  <7  _  v 

100  are  equal  respectively  to  —  r  —  and    ^  .     These  coefficients 


will  always  indicate  by  their  values  whether  we  are  working  with 
the  proper  tabular  values.  Numerator  and  denominator  of  the 
fraction  should  always  be  positive,  and  the  value  of  the  fraction  less 
than  unity. 

218.  The  Solution  of  Problems.  —  With  the  ballistic  formulas 
and  the  tables,  the  solutions  of  the  problems  of  gunnery  become 
very  simple.  We  will  remember  that  all  the  functions  in  Table  II 
are  functions  of  V  and  of  Z  =  X/C,  the  arguments  of  the  table. 
Therefore,  given  any  two  of  the  three  quantities,  V,  Z,  and  a  value 
of  a  function,  the  third  may  be  determined  from  the  table,  and 
also  the  corresponding  value  of  any  other  function  in  the  table. 
For  instance,  suppose  V  and  A'  are  given  and  the  corresponding 
values  of  A",  log  E'  and  T'  are  required.  With  V  and  A'  we  may 
obtain  Z  from  the  table,  and  with  V  and  Z  we  obtain  A",  log  B' 
and  T. 

Inspecting  the  formulas,  pages  376  and  377,  we  select  those  that 
contain  the  given  quantities,  and  such  other  formulas  as,  with 
Table  II,  will  enable  us  to  pass  to  the  formula  containing  the 
required  quantity. 

It  must  be  remembered  that  in  the  formulas  the  large  letters 
represent  values  of  the  quantities  for  the  whole  range,  or  complete 
horizontal  trajectory;  while  the  small  letters  represent  values  of 


•  EXTERIOR  BALLISTICS.  381 

the  same  quantities  for  particular  points  of  the  trajectory.  In  the 
tables  all  these  values  are  gathered  in  columns  headed  with  the 
large  letters,  which  are  thus  used  in  a  general  sense. 

In  what  follows,  either  in  general  discussions  or  when  demon- 
strating the  use  of  the  tables,  the  large  letters  will  be  used. 

To  show  the  advantages  derived  from  the  use  of  Table  II  with 
the  abbreviated  formulas,  let  us  consider  the  problem  whose  solu- 
tion by  means  of  Table  I  has  been  indicated  on  page  372. 

219.  Problem  i. — What  is  the  time  of  flight  of  a  3-inch  pro- 
jectile weighing  15  Ibs.,  for  a  range  of  2000  yards;  muzzle  velocity, 
1700  feet? 

C  =  15/9,  7  =  1700,  and  Z  =  6000  are  given.     T  is  required. 
These  formulas  apply:  T  =  CT'sec  $  (33) 

sin2<£  =  AC  (34) 

Z  =  X/C  (40) 

Determine  Z  from  (40). 
With  Z  and  V  take  A  and  T'  from  Table  II. 
Determine  <f>  from  (34). 

Determine  T  from  (33).  Ans.  T  =  4AS  seconds. 

Compare  this  with  the  process  indicated  on  page  372. 
To  show  the  most  convenient  method  of  performing  the  work, 
the  solution  of  a  problem  is  here  given  in  full. 

220.  Problem  2.— A  575  Ib.  projectile  is  fired  from  a  10-inch 
gun  at  a  target  8000  yds.  distant;  muzzle  velocity,  2540  f.  s.    As- 
suming the  atmospheric  conditions  as  normal,  determine  the  angle 
of  elevation  required  and  the  other  ballistic  elements. 

No  data  being  given  for  the  determination  of  d^/d,  and  the 
correction  for  altitude  not  being  required,  the  value  C  =  w/d2  is 
taken  for  the  ballistic  coefficient. 

log  w    2.75967 
2  log  d    2.00000 

log  C    0.75967 
Z  =  X/C  log*    4.38021 

log  Z    3.62054 

Z  =  4173.9 


382  ORDNANCE  AND  GUNNERY. 

To  find  the  angle  of  departure,  use  sin  2  <f>  =  AC. 
From  Table  II,  with  7  =  2540  and  Z  =  4174, 

A  =  (0.03054)  +  . 74X107- .4X243-. 3X10  =  0.03033 
The  inclusion  of  the  number  in  parentheses  is  to  indicate  that 
in  applying  the  corrections  this  number  is  treated  as  a  whole 
number. 

log  A    2.48187 
log  C    0.75967 


log  sin  2  0    1 . 24154  2^  =  10°  2'.6 

0=  s°r 

<j>,  after  being  accurately  determined,  is  used  to  the  nearest 
minute  only. 

To  find  the  time  of  flight,  use  T  =  CTf  sec  <£. 
From  Table  II,  with  V  and  Z, 

T'  =  (2.145)  +  .  74X68-  .4X89-.  3X3  =  2.1588 

log  T    0.33421 

logC    0.75967 


1.09388 
log  cos  <£     1.99833 


log  T    1. 09555        T  =  12 . 46  seconds 
To  find  the  angle  of  fall,  use  tan  w  =  B'  tan  <£. 
From  Table  II,  with  V  and  Z,  (Jvi  —  Jvo)  being  negative, 
log  B'  =  (0.1513)  +  .74X38-.4X12  +  . 3  =  0.15366 

log  E'    0.15366 
log  tan  (f>    2.94340 


log  tan  a>    1 . 09706  10  = 

To  find  the  striking  velocity,  use  v  =  u  cos  <j>  sec  0. 
6  in  this  case  becomes  a>.     From  Table  II,  with  V  and  Z, 
u  =  1481  -.74X20  +  .4X66  =  1492.6 

logw    3.17394 
logcos«jS    1.99833 


3.17227 
log  cos  to    1.99663 

logu    3.17564  v  =  1498  La. 


EXTERIOR  BALLISTICS.  383 

It  is  evident  from  these  values  of  u  and  v  that  no  material  error 
is  made  by  considering,  for  this  shot,  that  u  =  r. 

To  find  the  maximum  ordinate,  use  y0  =  a0"  C  tan  <j>. 

As  already  explained,  see  equation  (39),  we  find  the  value  of 
do"  in  this  equation  by  means  of  the  value  A  obtained  from  the 
equation  sin  2  (f>  =  AC.  At  the  summit,  see  equation  (38), 


This  value  of  A  is  therefore  the  value  of  A'  for  the  summit. 
Using  this  value  of  A  in  the  A'  column  of  Table  II,  with  the  given 
value  of  V,  we  obtain  from  the  A"  column  the  value  of  a0". 

The  value  of  A  obtained  above  is  0.03033 

From  Table  II,  with  7  =  2540  and  A'  =  0.0303, 

2200 

Z-Zp     303  -(300  -.4X24)^ 
100  18-  .4 

a0"  =  1200  +.71X59  =  1241.9 
logao"     3.09409 
log  C    0.75967 
log  tan  c£    2.94340 

log  7/0    2.79716  ?/o  =  626.  8  feet 

221.  Problem  3.  —  Compute  the  drift  for  the  shot  in  Problem  2. 
Use  Mayevski's  formula,  D  (yds.)  =  [5.  79239]  C2D'/cos3  <£. 

7  =  2540        Z  =  4174        <£  =  5°  1'        log  C  =  0.75967 

From  Table  II        £>'  =  81  +  .74X5-.4X6  =  82.3 

logD'    1.91540 

2  log  C    1.51934 

const.log    3.79239 

1.22713 

3  log  cos  0    1.99499 

log  D    1  .  23214  D  =  17  yards 

222.  Correction  for  Altitude.—  The  altitude  factor  /  in  the  bal- 
listic coefficient,  see  equation  (42),  takes  into  account  the  diminution 
in  the  density  of  the  air  as  the  projectile  rises,  and  it  corrects  with 
sufficient  exactness  for  the  error  that  arises  from  the  use  of  the 


384  ORDNANCE  AND  GUNNERY. 

Standard  density  with  which  Table  II  is  computed.  When  accu- 
racy is  desired  the  altitude  factor  is  calculated  and  applied  to  the 
ballistic  coefficient  in  all  firings  at  angles  greater  than  about  5 
degrees. 

Under  the  assumption  of  the  mean  height  of  the  trajectory  as  two 
thirds  of  the  maximum  ordinate,  the  value  of  the  altitude  factor  is 
given  by  the  equation 

log  (log  /)=log  2/o+5.  01765  [44] 

The  summ't  ordinate  is,  equation  (39), 
yQ  =  a0"  C  tan  (j> 

As  C  enters  the  value  of  y0  we  must  assume,  lor  an  approxi- 
mation in  the  determination  of  the  altitude  factor  by  means  of 
equations  (39)  and  (44),  the  value  of  C  obtained  by  considering 
the  altitude  factor  as  unity.  Call  this  value  C\.  With  Ci  com- 
pute 0  as  explained  in  Problem  2,  determine  y0  from  equation  (39) 
and  /  from  (44).  Call  these  values  <f>i,  y0i,  and  /i.  Then  applying 
the  value  /i,  thus  determined,  to  the  assumed  value  Ci,  a  new 
value  of  C,  Cc,  is  obtained.  This  value  Cc  will  be  close  to  the  true 
value  and  may  usually,  with  sufficient  accuracy  for  practical  pur- 
poses, be  used  as  C.  If  greater  accuracy  is  desired  a  second  deter- 
mination (of  (f>c,  y0c,  and  /c)  is  made.  The  resulting  value,  fc,  is 
applied  to  the  value  C\  first  assumed,  and  the  process  is  repeated 
until  there  is  no  material  change  between  the  corrected  values  of 
Ci  resulting  from  the  last  two  operations.  The  final  corrected 
value  is  then  used  as  C. 

223.  Problem  4.  —  Correct  the  ballistic  coefficient  for  altitude, 
and  determine  the  angle  of  elevation  required  in  order  that  a 
1048  Ib.  projectile  fired  from  the  12  inch  rifle  with  a  muzzle  velocity 
of  2350  f.  s.  may  strike  a  target  distant  12,000  yds.;  the  atmos- 
pheric conditions  at  the  time  of  firing  being  barometer  29".5, 
thermometer  67°  F., 

d  =  l2        w  =  1048        X  =  36,000        F  =  2350 
The  process  may  be  indicated  as  follows  : 

Table  II,  4,  a0"        sin  2<f>  = 


yo=a0"  C  tan  0        log  (log  /)  =log  y0+5.  01765 


EXTERIOR  BALLISTICS.  385 

Table  VI          *i/a  =  1.037  -0.5  (1.037  -1.003)  =  1.02 

A  w 
C  =  f~dd?  log*/*    0.00860 

Consider  c  =  l  log  w     3.02036 


3.02896 
log  d2     2  .  15836 


logCi     0.87060     (1st  approximation) 
Z  =  X/C  logZ     4.55630 


log  Z    3.68570  Z  =  4849.5 

Table  II,  A  =  (0.04589)  +  .  495X146-.  5X396-.  248X13  =  0.  044601 

While  using  the  table  we  will  take  out  for  future  use  the  value  of 
a0"  corresponding  to  a0'  =  A  =  0.044601. 

With  a0'  =  0.044601,  we  obtain  from  the  A'  column 


2600 

Zp       446-  (447-.  5X38) 


100  24-.  5X2 


Note  mat  in  this  operation  we  have  taken  a  tabular  value 
0.0447  for  A  larger  than  the  given  value  0.0446  because  the  tabular 
value  when  corrected  for  the  variation  in  V  becomes  less  than  the 
given  value. 

a0"  =  1444  +  .783  X  61  =  1491.8 

sin  20  =  AC  log  A    2.64934 

logCi    0.87060 


log  sin  20!     1 . 51994  2  &  =  19°  20'.  1 

&  =  9°  40' 

2/o  =  ao"  ^  tan  0         log  tan  fa     1.23130 

logCi    0.87060 
Ioga0"    3.17371 


log  2/01     3.27561 


386  ORDNANCE  AND  GUNNERY. 

log  ?/oi     3.27561 
log    (log  /)=log  T/o+5.01765     5.01765 


log  (log  A)     2.29326 


log/!     0.01965 
logCi    0.87060 


log.Cc    0.89025     (1st  correction) 

With  the  corrected  value  of  C  we  repeat  the  process  followed 
after  the  determination  of  C\,  the  first  approximation. 

Z  =  X/C  logX    4.55630 

logCc    0.89025 


log  Z    3.66605  2  =  4635 

Table  II,    A  =  (0.04306)  +  .35X140-.5X372-.175X12  =  0.041669 

Take  out  for  future  use  the  value  of  do"  corresponding  to  ao'  = 
A =0.04167 

2500 

Z-Z0       416.7- (424-. 5X36) 


100  23-. 5X2 

a0"  =  1383 + .486  X  61  =  1412.6 

sin  20  =  AC  log  A    2.61981 

logCc    0.89025 


=  .486 


log  sin  2  <f>e    1.51006  2  0C  =  18°  53'.0 

0C  =  9°26'.5 

7/0  =  a0"  C  tan  0         log  tan  0  c    1 . 22088 

logCc    0.89025 
loao'7     3.15002 


Iog7/oc    3.26115 
log  (log  /)  =  log  t/o+ 5. 01765         5.01765 


log  (log /c)     2.27880 


log/c    0.01900 
logCi    0.87060 


logCcc     0.88960    (2d  correction) 


EXTERIOR  BALLISTICS.  387 

As  this  value  of  log  Ccc  does  not  differ  greatly  from  the  value 
log  Cc  =  0.89025,  obtained  by  the  first  correction,  further  correction 
is  unnecessary  and  we  will  use  log  Ccc  as  log  C  in  determining  the 
angle  of  departure. 

Z  =  X/C        Table  II,  A        sm2<f>  =  AO 

log.Y    4.55630 
log  C    0.88960 

logZ    3.66670  Z- 4641. 9 

A  =  (0.04306)-f. 419X140-. 5X372-. 21X12=0.041761 
sin  20  =  AC  log  A    2.62077 

log  C    0.88960 

log  sin  2  0     1 . 51037  2  <j>  =  18°  53'.8 

<}>=  9°26'.9 

This  value  of  <j>  is  practically  the  same  as  the  value  <J>C  pre- 
viously obtained.  It  is  obvious  therefore  that  we  have  carried 
the  correction  for  altitude  sufficiently  far. 

224.  ANGLE  OF  DEPARTURE  CONSTANT. — When  the  angle  of 
departure  <f>  is  fixed,  instead  of  the  range  X  as  in  the  last  problem, 
the  correction  for  altitude  is  made  and  the  range  found  as  here 
indicated. 

C  =  f^~     A  =  sin  2  <f>/C    Table  II,  a0"    y0  =  aQ"  C  tan  0 
log  (log  /)  =log  i/o+5.01765      X  =  ZC 

Determine  Ci  from  C  =  wdl/dd2,  as  in  Problem  4  (1st  approxima- 
tion). 

Find  a0'  =  A  from  sin  2  (f>  =  AC 

Find  a0"  corresponding  to  a0'  from  Table  II 

Find  ?/oi  from  j/o  =  «</'  C  tan  <j> 

Find  /i  from  log  (log  /)=log  y0+ 5.01765 

Find  Cc  from  Ce  =  f\C\  (1st  correction) 
and  proceed  in  the  same  way  to  find  Ccc  or  C%c  as  required. 

Find  the  range  from  X  =  ZC  with  the  final  corrected  value  of  C. 

225.  The  Effect  of  Wind. — In  considering  the  wind  we  assume 
that  the  air  moves  horizontally,  and  that  the  effect  on  the  velocity 
of  the  projectile  is  due  to  the  component  of  the  wind  in  the  plane 


388  ORDNANCE  AND  GUNNERY. 

of  fire  only.     We  also  assume  as  practically  correct  that  the  time 
of  flight  of  the  projectile  is  not  influenced  by  the  wind. 
Let  W  be  the  velocity  of  the  wind  in  foot  seconds, 
Wp  the  component  of  W  in  the  plane  of  fire, 
a  the  angle,  reckoned  from  the  target,  between  the  direc- 

tion of  the  wind  and  the  plane  of  fire. 
Then 

WP  =  W  cos  a. 

Call  Wp  positive  for  a  wind  opposed  to  the  projectile,  and  nega- 
tive for  a  wind  with  it. 

THE  EFFECT  ON  RANGE.  Ingall's  Method.  —  We  will  assume  that 
the  effect  of  the  wind  component,  Wp,  is  simply  to  increase  or 
diminish  the  resistance  encountered  by  the  projectile;  and  that 
therefore  this  resistance,  instead  of  being  due  to  the  velocity  v,  is 
due  to  the  velocity  (v±  Wp).  Represent  by  AX  the  correction  to 
be  applied  to  the  range  in  a  calm  to  produce  the  true  range,  this 
correction  being  the  variation  in  range,  with  its  sign  changed, 
caused  by  the  wind.  We  may  put  equations  (23)  and  (22),  when  <f> 
is  small  and  cos  (f>  nearly  unity,  in  the  following  forms,  using  the 
upper  signs  when  the  direction  of  Wp  is  toward  the  gun  and  the 
lower  signs  when  it  is  toward  the  target. 


AX  =  C\S(v±Wp)-S(V±Wp)}-(X±TWp) 

in  which  T(v±Wp)  and  S(v±Wp)  are  the  T  and  S  functions  in 
Table  I. 

Compute  the  range  X  and  the  time  of  flight  T  without  consider- 
ing the  wind.  Then  from  the  first  of  the  foregoing  formulas  find 
v±Wp,  and  from  the  second  the  desired  value  of  AX. 

226.  Another  Method.  —  Let  ob,  Fig.  159,  represent  the  initial 
direction  of  the  projectile  and  its  velocity  V.  Let  be  represent  the 
velocity  Wp  of  the  wind  component  in  the  plane  of  fire,  reversed 
in  direction  While  the  projectile  moves  from  o  to  6  the  air  par- 
ticle b  moves  to  the  left  a  distance  equal  to  be.  The  direction  of 
movement  of  the  projectile  relative  to  this  particle  of  air  is  there- 
fore oc,  which  is  also  the  relative  velocity,  V,  of  the  projectile. 
<f>'  is  the  relative  inclination,  and  J</>  the  relative  change  in  inclina- 


EXTERIOR  BALLISTICS. 


389 


tion.     Draw  cd  perpendicular  to  ob,  and  call  bd  AV.    Then,  using 
the  upper  signs  only, 


V'  =  V±AV  (nearly) 
V'sin  4<>  =  Wsm(> 


(45) 
(46) 
(47) 
(48) 


FIG.  159. 

Referring  to  Fig.  160,  let  b  represent  the  position  of  the  gun, 
and  bd  the  range  X  in  calm  air.  In  the  head  wind  the  range  is 
reduced  to  be.  cd  is  therefore  the  variation  in  range  due  to  the 
wind.  While  the  projectile  travels  from  6  to  c  the  air  particle 
travels  from  6  to  a,  the  distance  WPT.  ac,  or  X',  is  therefore  the 
distance  that  separates  the  projectile  and  the  air  particle  at  the 


FIG.  160. 

end  of  the  time  T;  that  is,  it  is  the  relative  range  of  the  projectile 
with  respect  to  the  air  particle.  The  relative  initial  velocity  of 
the  projectile  is  as  shown  in  Fig.  159,  its  velocity  in  a  calm,  V,  in- 
creased by  the  component  AV  of  the  air's  velocity  in  the  direction 
of  motion.  V'  =  V+AV  is  therefore  the  initial  velocity  necessary 
to  produce  the  relative  range,  and  similarly  <j>'  =  <f>—J<j>  is  the 
necessary  angle  of  departure. 


390  ORDNANCE  AND  GUNNERY. 

It  is  apparent  from  Fig.  160  that 

cd  =  bd—bc  =  bd—  (ac—  ab) 
or  cd  =  X-(X'-WpT] 

and  calling  cd  with  its  sign  changed  AX,  we  have 


Compute  the  relative  range  X'  with  the  values  V  and  $',  using 
the  formulas  with  Table  II.  While  the  projectile  is  traversing  this 
relative  range  the  air  particle  moves  over  a  distance  WPT.  The 
actual  range  traversed  by  the  projectile  is  therefore  Xf  T  WPT,  and 
the  variation  in  range  due  to  the  wind  is 


Changing  the  sign  and  rearranging,  we  get 

AX  =  X'-(X±WPT)  (49) 

in  which  X  and  T  are  computed  from  V  and  <f>  without  considering 
the  wind. 

The  upper  signs  in  the  above  equations  apply  when  the  wind 
blows  toward  the  gun,  the  lower  signs  when  it  blows  toward  the 
target. 

APPLICATION  OF  METHODS.  —  The  first  method  of  obtaining  the 
variation  in  range  due  to  wind  is  useful  only  when  the  angle  of 
departure  is  small.  The  second  method  may  be  used  in  all  prob- 
lems of  direct  fire. 

227.  Problem  5.  —  What  will  be  the  effect  of  a  one  o'clock  wind, 
blowing  30  miles  an  hour,  on  the  range  of  the  shot  in  Problem  1  ? 
Velocity  in  miles  per  hour  X  44/30  =  velocity  in  foot  seconds. 

W  =  30x44/30  =  44  f.  s.        «  =  30° 
WP  =  W  cos  a  =  38.1  f.  s. 

From  Problem  1:  log  C  =  0.22185,  Ar  =  6000,  F  =  1700, 
7T=4.48,  0  =  2°  42' 

Therefore    WPT  =  17Q.7,    and    X+WPT  =  G170.7 

First  Method.          V+  W  p  =  1738.  1 


EXTERIOR  BALLISTICS.  391 

From  Table  I,    5(1738.  1)=6220.  2-  .81X43.8  =  6184.7 
7X1738.1)=  2.  508-  .  SIX.  025  =  2.  4878 
log?1      0.65128 
logC      0.22185 


logT/C      0.42943  77(7  =  2.6880 

7X1738.1)     2.4878 


T(v+Wp)     5.1758 
From  Table  I, 


and          5(1113.  4)  =  9860.  0-  —  X20.  6  =  9845.  6 

5(1113.4)        9845.6 
5(1738.1)        6184.7 


log    3660.9  3.56359 

logC  0.22185 

log    6101.5  3.78544 

X+WPT    6170.7 


JX=-69.2  feet 
228.  Second  Method.—  Find 
Equation  (45)  J7  =  38.06 

(46)  7'  -1738.1 

(47)  J<£  =  3'.6 

(48)  <//  =  2°38'.4 
From  sin  2<£'  =  AG  A  =  0.05521 
From  Table  II  Z  =  3671.5 
FromZ-X'/C                            X'-6119.1 


Equation  (49)  JX=-51.6  feet 

Note  the  difference  in  the  results  of  the  two  methods.     Neither 
method  is  wholly  satisfactory. 


392  ORDNANCE  AND  GUNNERY. 

229.  THE  EFFECT  OF  WIND  ON  DEVIATION.  —  The  component  of 
the  wind  perpendicular  to  the  plane  of  fire,  W  sin  a,  is  alone  con- 
sidered as  producing  deviation.  The  deviation  due  to  the  wind 
can  only  be  determined  by  experiment  for  each  kind  of  projectile. 

The  following  formula  for  the  deviation  of  8,  10,  and  12  inch 
projectiles  is  given,  in  another  form,  in  the  Coast  Artillery  Drill 
Regulations. 


(TYseo^        \2 
33000-U(yds.))    (50) 

in  which      W  is  the  velocity  of  the  wind  in  miles  per  hour, 
a    its  angle  with  the  plane  of  fire, 
T  is  the  time  of  flight  in  seconds, 
X  the  range  in  yards. 

Problem  6.  —  Compute  the  deviation  of  the  shot  in  Problem  2 
for  a  two  o'clock  wind  blowing  20  miles  an  hour. 

TF=20m.p.h.        a  =  60°        W  sin  a  =  17.32        T  =  12.46 

(12  46       \2 
33000  +  80007  ==16yards>  left- 

230.  The  Danger  Space.  —  The  danger  space  is  the  horizontal 
distance  over  which  an  object  of  a  given  height  will  be  struck.  It 
is  the  horizontal  length  of  those  portions  of  the  trajectory  for  which 
the  ordinates  are  equal  to  and  less  than  the  given  height.  Usually 
the  danger  space  at  the  further  end  of  the  range  is  alone  con- 
sidered. 

The  elements  of  the  trajectory  are  assumed  to  be  known. 

Let  dbc,  Fig.  161,  be  the  known  trajectory  for  the  range  X,  and 


y. 


-x 

X- 

FIG.   161. 


let  y  represent  the  height  of  the  object  for  which  the  danger  space 
is  to  be  determined.  The  danger  space  for  this  height  is  evidently 
so  much  of  the  range  as  lies  beyond  the  ordinate  y.  It  is  equal  to 


EXTERIOR  BALLISTICS. 


393 


the  whole  range  minus  the  abscissa  x  corresponding  to  the  ordinate 
y.  Calling  the  danger  space  AX  we  obtain  AX  =  X-x. 

The  problem  of  determining  the  danger  npace  therefore  con- 
sists in  finding  the  value  of  x  corresponding  to  the  given  value  of 
y  and  subtracting  from  the  given  range. 

Substituting  Cz  for  x  in  equation  (37)  and  combining  with 
equation  (34)  we  obtain 

(A-a}z  =  2ycos2<j>/C2  (51) 

in  which  A  is  the  value  of  the  function  for  the  whole  range  X,  and 
a  the  particular  value  of  the  same  function  for  the  abscissa  x  cor- 
responding to  the  ordinate  y.  The  elements  of  the  whole  range 
being  known,  and  y  given,  the  second  member  of  the  above  equa- 
tion is  known,  and  A  in  the  first  member.  There  remain  two 
quantities,  a  and  z,  to  be  determined  from  the  equation.  This  is 
done  by  applying  the  method  of  double  position. 

231.  METHOD  OF  DOUBLE  POSITION. — Enter  Table  II  with  the 
known  value  of  V.  Inspect  the  table  and  find  a  value  of  Z  which 
when  substituted  with  its  corresponding  value  of  a  from  the  A 
column  in  the  first  member  of  equation  (51)  will  give  to  that 
member  a  value  close  to  the  known  value  of  the  second  member. 
The  difference  between  the  first  and  second  members  is  the  error. 
Repeat  this  operation  until  two  successive  values  of  Z  are  found, 
ZQ  and  Zi,  that  give  values  for  the  first  member,  one  value  greater 
and  one  less  than  the  value  of  the  second  member. 

Let  ZQ  and  Zi,  Fig.  162,  represent  these  values  of  Z;  F0  and  F\ 
the  resulting  values  of  the  first  member  of  equation  (51);  and  S 
the  known  value  of  the  second 
member.  e0  and  e\  will  represent 
the  errors  obtained  with  FQ  and 
FI.  It  is  evident  from  the  figure 
that  the  true  value  of  Z  lies  be- 
tween ZQ  and  Zi  and  that  its  dis- 
tance from  the  smaller  trial  value 
ZQ  is  given  by  the  proportion 

Z-Z0 


FIG.  162. 


Solving  for  Z 


(52) 


394  ORDNANCE  AND  GUNNERY. 

In  the  application  of  this  method  to  equation  (51)  we  are  assuming 
that  (A—  a)z  varies  proportionately  with  z  between  the  values  Z0 
and  Zi.  This  is  not  a  true  assumption,  but  the  results  are  suffi- 
ciently approximate  for  practical  use. 

To  make  this  demonstration  general  we  may  consider  that  z 
and  (A  —  a)  in  equation  (51)  represent  any  two  functions,  /  and  /', 
whose  product  is  known.  We  then  have 

ff-k 

We  may  write  either  /  or  /'  for  Z  in  equation  (52)  and  obtain 
the  general  formula 


We  may  now,  employing  the  method  of  double  position,  deter- 
mine from  equation  (52)  the  value  of  z  in  (51),  and  from  the  equa- 
tion z  =  x/C  we  obtain  the  value  of  x  corresponding  to  the  given 
ordinate  y.  We  then  have  for  the  danger  space 

AX  =  X-x  (54) 

232.  Problem  7.  —  What  is  the  danger  space,  for  an  infantry- 
man, in  the  1000  yard  trajectory  of  the  service  0.30  caliber  rifle; 
muzzle  velocity,  2700  f.  s.;  bullet,  150  grains? 

This  assumes  that  the  rifle  is  fired  from  the  ground. 

The  height  of  a  man  is  assumed  at  5'  8"  =  5.67  feet  =  y. 

The  value  of  the  coefficient  of  form  c,  in  the  ballistic  coefficient, 
as  determined  by  experiment  for  the  150  grain  bullet  is  c  =  0.5694, 
see  foot-note. 

w  =  150/7000        d  =  0.3        7  =  2700        X  =  3000 

The  coefficient  of  form  is  determined  for  the  small  arms  bullet  by  means  of 
actual  measurements  of  the  velocity  of  the  bullet  at  the  ends  of  a  long  range, 
as,  for  instance,  500  yards.  With  the  measured  values  of  V  and  v,  the  latter 
corrected  for  the  effect  of  wind  if  there  is  any,  and  the  measured  range,  the 
value  of  C  is  determined  from  the  equation  x=C\S(v)  —  S(V)\  by  means  of 
ballistic  Table  I.  The  coefficient  of  form  c  is  then  obtained  from  the  equation 

r=d1  w_ 
d  cd2 

For  the  projectiles  of  large  guns  the  coefficient  c  is  determined  by  means 
of  measured  values  of  (f>,  V,  and  X,  see  Problem  12. 


EXTERIOR  BALLISTICS.  395 

The  steps  in  the  operation  are  indicated  as  follows: 

C  =  w/cd2        Z  =  X/C        Table  II,  A        sm2<f>  = 
(A-a}z=2ycos2<f>/C2        x=zC        AX=X-x 

C=w/cd2  log  7000    3 . 84510 

log  c      1 . 75542 
logd2    2.95424 


2.55476 
log  150    2.17609 


Z=X/0  log  C    1.62133 

logX    3.47712 


log  Z    3.85579  Z  =  7174.5 

Table  II,       A  =  (0.06201)4-0. 745X158=0. 063187 

sm2(f>  =  AC  log  A     2.80063 

log  C    1.62133 

log  sin  2  <f>    2 . 42196  20  =  1°  30'.8 

0  =  45'.4 

(A-a)z  =  2ycos2<f>/C2      \og2y    1.05461 
log  cos2  ^    1.99992 

1  05453 
logC2    1.24266 

1.81187  (A-a)z  =  64.844 

Applying  the  method  of  double  position  to  find  the  values  of 
z  and  a  that  will  satisfy  this  equation,  we  find  by  inspection  of 
Table  II  for  F  =  2700  that  the  value  of  Z  =  6500  with  the  corre- 
sponding value  of  A,  0.05307,  will  when  substituted  in  the  last 
equation  give  a  close  approximation  to  64.844. 
With  Z  =  6500  we  obtain 

(0.063187-0.05307)6500  =  65.761 
e0  =  65.761-64.844  =  0.917 

With  Z  =  6600 

(0.063187-  0.05449)6600  =  57.4 

=  64.844-57.4  =  7.444 


396  ORDNANCE  AND  GUNNERY. 

The  results  obtained  with  these  values  of  Z  are  greater  and  less 
than  64.844. 


Then  from  Z  =  ZQ+ 


0  Q17 

X100~6511 


444 

=  zC  log  z    3.81365 

logC    1.62133 


logo;    3.43498  z  =  2722.6 

AX=X-x          AX  =  3000  -2722.6  =  277.4  ft.  =  92.5  yds. 


For  7  =  2700  we  will  also  find  that  the  value  Z  =  1122.7  with 
the  corresponding  value  of  a  will  nearly  satisfy  the  equation 
(A—  a)z  =  64.844.  This  value  of  z  gives  x  =  469.5  feet,  which  is 
at  once  the  danger  space  at  the  inner  end  of  the  trajectory,  see 
Fig.  161. 

233.  The  Danger  Range.  —  When   the  danger  space  is  con- 
tinuous and  coincides  with  the  range  it  is  called  the  danger  range. 
Thus  the  danger  range  for  an  infantryman  is  the  range  at  every 
point  of  which  an  infantryman  would  be  struck.     The  maximum 
ordinate  of  the  trajectory  is  therefore  5  feet  8  inches. 

To  determine  the  danger  range  we  compute  the  horizontal  tra- 
jectory whose  maximum  ordinate  ?/o  is  given. 

Combining  equations  (34)  and  (39)  and  making  cos  <£  unity, 
since  $  for  all  danger  ranges  is  very  small,  we  obtain 

a0'ao"  =  2y0/C2  (55) 

From  this  we  determine  o</  by  trial  by  the  method  of  double 
position,  using  the  A'  and  A"  columns  of  Table  II.  Since  at  the 
summit  ao'=A,  see  (38),  with  this  value  of  a</  we  go  to  the  A 
column  of  Table  II  for  the  given  value  of  V  and  find  the  correspond- 
ing value  of  Z,  from  which  the  required  X  is  obtained. 

234.  Problem  8.  —  What  is  the  danger  range,  for  a  cavalryman, 
of  the  service  rifle  fired  from  the  ground?    The  height  of  a  cavalry- 
man is  assumed  as  8  feet. 

7  =  2700        log  0=1.62133        y0  =  S 


EXTERIOR  BALLISTICS.  397 

The  successive  steps  are  indicated  as  follows : 

aoW  =  27/o/C2        Table  II,  Z        X  =  ZC 

a0"  =  2y0/C2  log  2y0    1.20412 

log  C2     1.24266 


log  ooW     1  .  96146  a0V  =  91  .508 

By  inspection  of  Table  II  for  F  =  2700  we  find  that  the  product 
of  a0'  and  do"  for  Z  =  3400  will  give  a  close  approximation. 
For  Z  =  3400     a0'a0"  =  0  .  0467  X  1  938  =  90  .  504 

e0  =91.508-90.504  =  1.004 
For  Z  =  3500    a0'a0"  =  0  .  0488  X  2002  =  97  .  697 
ei  =  97.  697-91.  508  =  6.  189 
The  first  product  obtained  is  less  than  91  .  508  and  the  second 

product  greater.     In  /  =  /o  +  -     —  (/i  —  /o)  write  a</  for  /;   0.0467, 

" 


the  smaller  trial  value  of  a0',  for  /o;  and  0.0488  for  fa. 
a0'  =  (0  .  0467)  +          '  °°4  lgQ  X  21  =  0  .  04699 


or  it  may  sometimes  be  more  convenient  to  find  the  value  of  Z  and 
then  the  value  of  a0f.    Thus 


and  OQ'  =  (0  .  0467)  +.14X21=0.  04699 

Using  this  value  of  a0'  in  the  A  column,  we  obtain 


X=ZO  log  Z    3.78178 

log  C    1.62133 


logX    3.40311 

X  =  2529.  9  ft.  =  843.  3  yds. 


398  ORDNANCE  AND  GUNNERY. 

The  trajectory  for  this  range  is,  at  its  highest  point,  8  feet  from 
the  ground.  A  cavalryman  at  any  point  of  the  range  would  there- 
fore be  struck. 

235.  Curved  Fire.  —  Problems  involving  angles  of  departure 
less  than  30  degrees,  and  initial  velocities  less  than  825  f.  s.,  are 
solved  by  means  of  the  first  part  of  Table  II,  pages  14  to  16,  Bal- 
listic Tables.  The  formulas  to  be  used  are  collected  on  page  VIII 
of  the  tables  under  the  heading  "Formulas  to  be  used  with  the 
first  part  of  Table  II."  They  will  also  be  found  under  the  heading 
Curved  Fire  on  page  377,  ante. 

For  velocities  less  than  825  f.  s.  the  resistance  of  the  air  is 
assumed  to  vary  as  the  square  of  the  velocity,  or,  as  it  is  called, 
according  to  the  Quadratic  Law  of  Resistance.  Under  this  law  the 
formulas  for  direct  fire  are  capable  of  modification  into  the  forms 
that  we  are  now  considering. 

It  may  be  shown  that  under  the  quadratic  law  of  resistance 
the  function  A,  for  the  same  value  of  Z=X/C,  that  is,  for  the 
same  range  and  projectile,  will  vary  for  different  values  of  V  in 
the  ratio  Vi2/V2.  If  therefore  we  obtain  the  values  of  A  with  the 
value  Vi  and  all  the  necessary  values  of  Z,  we  can  pass  by  means 
of  the  above  ratio  to  the  value  of  A  for  any  other  velocity.  The 
value  Fi  =  800  was  used  in  calculating  the  part  of  Table  II  that 
refers  to  velocities  less  than  825  f.  s. 

The  value  of  sin  20,  see  equation  (34),  calculated  for  Vi  = 
becomes  for  any  other  velocity 


sin  2<f>  =  Ac  =  [5.  80618]  (56) 


the  form  in  which  it  appears  among  the  formulas  we  are  consider- 
ing. 

Under  the  quadratic  law  the  other  functions  vary  according  to 
different  ratios  of  V\  and  V,  as  shown  by  the  formulas  in  which 
they  appear.  Under  this  law  the  function  B'  becomes  independent 
of  the  muzzle  velocity,  and  therefore  V  does  not  appear  in  the 
formula  for  tan  to. 

CORRECTION  FOR  ALTITUDE.  —  In  curved  fire  the  correction  of  the 
ballistic  coefficient  for  altitude  is  made  by  the  same  process  as  in 


EXTERIOR  BALLISTICS.  399 

direct  fire,  but  using  the  value  of  sin  2<f>  given  by  equation  (56) 
instead  of  that  given  by  equation  (34). 

236.  Problem  9.  —  A  shot  is  fired  from  the  4.7  inch  siege  how- 
itzer at  a  target  4000  yards  distant;  w  =  QQ  Ibs.,  F  =  820  f.  s.,  ba- 
rometer 29".  6,  thermometer  63°.  Correct  the  ballistic  coefficient 
once  for  altitude  and  find  the  angle  of  departure  and  the  time  of 
flight. 

The  process  of  correcting  for  altitude  may  be  indicated  as 
follows  : 

C  =  &  ^-     Z  =  X/C     Table  II,  A,  a0"      sin  20  =  [5.80618]^C/F2 
o  cd 

7/0  =  a0"C  tan  <£        log  (log  /)  -log  i/o  +  5.01765 
Table  VI,       d^/d  =  1.029-0.6(1.029-0.994)  =  1.008 

C=/|^  logV*    0.00346 

=  !        c  =  l  low     1.77815 


1.78161 
logd2     1.34420 


log  Ci     0.43741        (1st  approximation) 
Z  =  X/C  logX    4.07918 

log  Z    3.64177  Z  =  4383 

Table  II,        A^  =  (0 . 24821)  +  .  83  X  662  =  0 . 25370 

A  =  a0'        With  OQ'  =  0 . 25370  find  a0". 


2200 

Z-Z0    2537-2456 


=  .66 


100  123 

.  66X53  =  1173 


log  A  1.40432 
logCi  0.43741 
const.  5.80618 

'  5.64791 


400  ORDNANCE  AND  GUNNERY. 

log  V2    5.82762 


log  sin  20    1 . 82029  2&  =  41°  23'. 2 

&=20°41'.6 
Ioga0"     3.06930 
logCi     0.43741 
log  tan  &     1 . 57719 


log  2/01     3.08390 
log  (log  /)=log  t/o  +  5.01 765          5.01765 


log  (log  A)     2.10155 


log  /!     0.01263 
logCi     0.43741 


logCc    0.45004 

We  will  use  this  as  log  C  in  determining  the  angle  of  departure  and 
time  of  flight. 

Z  =  X/C        Table  II,  A,  T 

sin  2<£  =  [5.80618]AC/F2         T  =  [2.90309]  CT'/V  cos  c> 

Z  =  X/C  logX    4.07918 

log  C    0.45004 


log  Z     3.62914  Z  =  4257.4 

Table  II,        A  =  (0 . 24163)  +  .  574  X  658  =  0 . 24541 
sin2<jS=[5.80618]AC/72 

log  A  1.38989 
log  C  0.45004 
const.  5.80618 


5.64611 
logF2    5.82762 


log  sin  2  0    1 . 81849  2<£  =  41°  HX.7 

0  =  20°35'.4 
=  [2.90309]Cr/Fcos0 


EXTERIOR  BALLISTICS.  401 

Table  II,        T'  =  (5.801)+  .574X152  =  5.8882 

logr    0.76998 

logC    0.45004 

const.     2.90309 


4.12311 
log  V  cos  <£    2 . 88514 


log  T7    1.23797 

T  =  17. 3  seconds 

237.  High  Angle  Fire.— Problems  in  high  angle  fire  are  solved 
by  means  of  Table  IV.  This  table  was  computed  under  the  quad- 
ratic law  of  resistance  and  is  practically  a  range  table,  for  veloci- 
ties less  than  825  feet,  for  a  projectile  whose  ballistic  coefficient  is 
unity.  To  make  it  applicable  to  other  projectiles  the  tabular 
numbers  involve  the  value  of  the  ballistic  coefficient  with  the 
values  of  the  different  elements.  Therefore  with  C  known,  and 
applied  as  indicated  in  the  headings  of  the  columns,  we  may,  with 
any  other  known  element  of  the  trajectory  in  addition  to  the  ele- 
vation, obtain  from  the  different  columns  the  values  of  the  remain- 
ing elements. 

Thus  C,  (f>,  and  V  being  known,  find  V /\/C  and  take  out  of 
Table  IV,  for  the  particular  value  of  <£,  the  values  of  X/C,  T/\/C, 
etc.,  corresponding  to  V/\/C  as  obtained.  X,  T,  etc.  may  then 
be  obtained.  If  <£  is  not  a  tabular  value,  solve  the  problem  for 
the  tabular  values  of  <£  on  either  side  of  the  given  value  and 
interpolate  between  the  results. 

To  correct  for  altitude  use  the  formulas  log  ,(log  /)  given  at 
the  head  of  each  table.  The  value  of  the  maximum  ordinate  is 
also  there  given  in  the  terms  of  the  range. 

THE  COEFFICIENT  OF  REDUCTION. — While  the  quadratic  law  of 
resistance  applies  to  velocities  less  than  825  f.  s.,  Table  IV  may  be 
used  for  the  higher  velocities  now  obtained  from  our  mortars  by 
the  introduction  of  the  coefficient  of  reduction  c  into  the  ballistic 
coefficient.  Compensation  may  thus  be  made  for  the  errors  arising 
from  the  use  of  the  table  for  higher  velocities.  The  coefficient  of 
reduction  is  actually  a  quantity  required  to  make  the  results 


402 


ORDNANCE  AND  GUNNERY. 


obtained  from  the  formulas  and  Table  IV  agree  with  the  results 
obtained  in  experiment. 

The  values  of  c  for  the  1046  Ib.  mortar  projectile  have  been 
calculated  from  actual  firings  for  different  ranges  and  angles  of 
elevation.  The  determinations  were  made  from  firings  with  the 
12  inch  cast  iron  steel  hooped  mortar.  The  values  of  c  which  are 
given  in  the  following  table  therefore  apply  only  to  projectiles 
fired  with  the  velocities  used  in  this  mortar.  In  the  steel  mortar, 
model  1890,  higher  velocities  are  attained. 

The  method  employed  in  the  calculation  of  the  coefficient  of 
reduction  is  shown  in  Problem  12. 


VALUES  OF  THE  COEFFICIENT  OF  REDUCTION,  c,  FOR  THE  1046  LB. 
PROJECTILE  IN  THE  12  INCH  MORTAR;  DETERMINED  FROM 
ACTUAL  FIRINGS. 


Elevation, 
Degrees. 

Range  in  Yards. 

3000 

4000 

5000 

6000 

7000 

8000 

45 

1.59 

2.11 

1.93 

1.76 

1.53 

1.25 

46 

1.77 

2.20 

1.94 

1.76 

1.55 

1.28 

47 

1.93 

2.28 

1.94 

1.77 

1.57 

1.32 

48 

2.07 

2.34 

1.95 

1.78 

1.59 

1.36 

49 

2.19 

2.38 

1.95 

1.79 

1.61 

1.40 

50 

2.29 

2.41 

1.96 

1.80 

1.63 

1.44 

51 

2.39 

2.42 

1.97 

1.81 

1.66 

1.48 

52 

2.48 

2.42 

1.98 

1.82 

1.68 

1.52 

53 

2.56 

2.42 

1.99 

1.83 

1.71 

1.56 

54 

2.62 

2.42 

1.99 

1.84 

1.74 

1.61 

55 

2.66 

2.42 

2.00 

1.85 

1.77 

1.65 

56 

2.65 

2.41 

2.01 

1.86 

1.79 

1.70 

57 

2.64 

2.40 

2.02 

1.87 

1.82 

1.75 

58 

2.62 

2.38 

2.04 

1.88 

1.85 

1.80 

59 

2.59 

2.37 

2.05 

1.89 

1.88 

1.85 

60 

2.56 

2.35 

2.07 

1.90 

1.91 

1.91 

61 

2.53 

2.34 

2.09 

1.92 

1.95 

1.97 

62 

2.49 

2.32 

2.11 

1.94 

1.99 

2.04 

63 

2.45 

2.30 

2.13 

1.97 

2.04 

2.11 

64 

2.41 

2.28 

2.15 

2.01 

2.09 

2.18 

65 

2.37 

2.26 

2.17 

2.07 

2.15 

2.25 

238.  Problems  in  High  Angle  Fire. — When  C,  <j>,  and  V  or  X 
are  given,  to  determine  the  remaining  elements. 

I.  Given  C,  V,  and  X,  to  determine  <j>  and  the  other  elements. 


EXTERIOR  BALLISTICS.  403 

METHOD.  1.  With  the  given  data  find  Ci  =  w/d2,  V/Vd,  and 
X/d. 

2.  With  the  value  of  V/Vd  enter  Table  IV  and  find  by  in- 
spection in  consecutive  tables  two  values  of  X/C,  one  value  greater 
and  one  valueless  than  the  trial  value  already  determined. 

3.  Assume  the  lesser  of  the  elevations  for  the  two  tables  as  a 
first  trial  value  of  <f>,  determine  /  from  the  formula  at  the  top  of 
the  table  for  this  value  of  <jS  and  compute  Cc  from  Cc=fw/cd2. 

4.  Then,  using  the  value  of  Cc  as  C,  redetermine  V/VC  and 
X/C. 

5.  With  these  values  reenter  Table  IV  and  redetermine  as 
before  a  second  trial  value  of  0. 

6.  With  this  value  of  <£  and  the  given  value  of  X  compute  F. 

7.  If  the  computed  value  be  greater  than  the  given  value,  re- 
compute with  the  next  lesser  value  of  0;   if  less,  recompute  with 
the  next  greater  value.     The  given  value  of  F  will  usually  lie  be- 
tween the  two  values  thus  computed,  if  not  continue  the  process 
until  this  result  is  attained. 

8.  Then  interpolate  for  0,  assuming  it  to  vary  directly  with  F. 

9.  To  find  the  other  elements,  T,  a>,  and  vu,  use  the  tables  for 
the  values  of  (f>  on  each  side  of  the  value  just  determined.     Find 
the  values  of  these  elements  from  each  table,  and  interpolate  be- 
tween the  values  so  determined  for  the  values  corresponding  to 
the  determined  value  of  <jS. 

Problem  10.  —  A  projectile  weighing  1046  Ibs.  is  to  be  fired 
from  a  12  inch  mortar,  model  1888,  to  reach  a  target  at  a  range  of 
7180  yards.  Assuming  the  muzzle  velocity  to  be  950  f.  s.,  deter- 
mine the  angle  of  elevation  required. 

^  =  1046       d  =  l2        F  =  950       X  =  2154Q 

1.  d=w/d2  log  Ci  =0.86117 

V/Vd  =  352  .  48  X/d  =  2965  .  4 

2.  From  Table  IV, 

for  0  =  59°      and      F/\/C  =  352.48        X/C  =2971.  7 
0  =  60°  F/\/C  =  352.48        X/C  =  2914 


180 
3.  Assume  0  =  59°       Page  402,  c  =  1.88-          X  .03  =  1.8746 


404  ORDNANCE  AND  GUNNERY. 

log  (log  /)  =  log  X-  5 . 32914    log  X    4 . 33325 

const.     5.32914 


log  (log/)     1.00411 

log/    0.10095 
G=fw/d2c  log  w/d2    0 . 86117 

0.96212 
logc    0.27291 


logCc    0.68921 

4.  log  V    2.97772 

logVC~c    0.34461 

logTY\/C    2.63311     7/\/C  =  429.65 

logZ    4.33325 
logCc    0.68921 

log  X/C    3 . 64404        X/C  =  4406 

5.  From  Table  IV, 

for  <£  =  55°    and     7/\/C  =  429.65        X/C  =  4436.1 

0  =  56°  7/\/C  =  429.65        Z/C  =  4375.1 

Computed  F/\/C  =  429.65        X/C  =  4406.0 

6.  Assume     </>  =  55°        c  =  l. 77-  .18X  .12  =  1.7484 
log  (log /)=  log  X- 5. 40257    log  X    4.33325 

const.     5 . 40257 


log  (log/)     2.93068 

log/    0.08525 
C  =  /w/d2(7  log  w;/d2    0 . 86117 

0.94642 
logc    0.24264 


logCc    0.70378 
logX    4.33325 


log  X/C    3.62947    .Y/C-4260.6 


EXTERIOR  BALLISTICS.  405 


fi 
Table  IV,        V/VC  =  410  +  -p^j-  X  10  =  419  .  33 

log  V/VCl    2.62256 
0.35189 


log  7    2.97445         7  =  942.87 
7.  Assuming  0  =  56°        c  =  1.79-  .18X  .09  =  1.7738 
log  (log  /)  =  log  X  -  5  .  38029    log  X    4  .  33325 

const.      5.38029 


log  (log/)     2.95296 

log/    0.08974 
C  =  fw/d2c  log  w/d2    0  .  86117 

0.95091 
logc    0.24890 


logCc    0.70201 
logZ    4.33325 


logX/C    3.63124        Z/C  =  4278 

65 
Table  IV,        7/\/C  =  420+TggXlO=423.87 


2.62723 
0.35101 


log  V    2.97824         7  =  951.13 

8.  For    7  =  942.87,    <£  =  55°,    and    for    7  =  951.13,    <£  =  5 
Therefore  for  7  =  950 


9.  To  obtain  the  values  of  T,   to,  and  i>w,  corresponding  to 
0  =  55°51'.8,  enter  Table  IV  for  0  =  55°  and  <£  =  56°,  using  as 
arguments  the  values  of  7/VC  obtained  above  in  steps  6  and  7. 
For  <  =  55°:  For  0  =  56°: 

=  419.33  7/x/C  =  423.87 

=  19  81  +  0.93X0.44  =  20.219  r/\/C  =  20.656 

'  +  0.93XlO'  =  59°  8'.3  ^=60°  7'.9 

.  93X6  =  360.  58 


406  ORDNANCE  AND  GUNNERY. 

From  these  values  we  derive,  using  the  values  of  V?5  as  deter- 
mined in  steps  6  and  7, 

!T  =  45.462  !F  =  46.351 

w  =  59°8'.3  o,  =  60°7'.9 

1^  =  810.76  1^  =  818.43 

Interpolating  between  these  values,  that  correspond  to  ^  =  55° 
and  <£  =  56°,  we  find  for  </>  =  55°  51'.8 

7  =  45.46+^^(46.  35-45.  46)  =46.  2  seconds 
ou 

=  59°  59'.8 


vu  =  810  .  8+  -77Q-  X  7  .  61  =  817  .  4  foot  seconds 

239.  II.  Given  C,  V,  and  <j>,  to  determine  X  and  the  other  ele- 
ments. 

METHOD.  To  determine  the  value  of  the  coefficient  c  from  the 
table  on  page  402  we  must  know  both  <£  and  X.  In  this  problem 
X  is  unknown. 

1.  We  will  therefore  first  determine  from  Table  IV  an  approxi- 
mate value  of  X,  designated  Xl}  using  for  this  purpose  C\=w/d? 
and  the  tabular  value  of  (j>  next  greater  than  the  given  value. 

2.  Take  from  the   table  for  c  the  value  of   c  corresponding 
to  the  value  Xi  and  to  the  value  of  <f>  used  in  step  1.     Call  this 
value  c\. 

3.  Determine  a  second  approximate  value  for  the  ballistic  co- 
efficient C2  =  w/Cid2.    Correct  for  altitude  by  means  of  Table  IV, 
using  0  as  in  step  1  ;  and  with  the  corrected  coefficient,  €3,  deter- 
mine a  corrected  range,  X2.     This  corrected  range  will  be  suffi- 
ciently close  to  the  true  range  to  enable  us  to  obtain  approxi- 
mately the  correct  values  of  c  from  the  table.     This  has  been  the 
object  of  the  foregoing  steps. 

4.  With  the  corrected  range,  X2,  and  the  tabular  values  of  <£ 
on  each  side  of  the  given  value  take  new  values  of  c  from  the  table. 
Call  these  values  c2  and  determine  with  them  two  new  values  for 
C,  designated  C^=w/c2d2. 


EXTERIOR  BALLISTICS.  407 

5.  By  means  of  Table  IV,  for  the  values  of  $  on  each  side  of 
the  given  value,  correct  both  values  of  C4  for  altitude.     Call  the 
resulting  values  C5. 

6.  Using  the  values  C5  as  C  find  the  corresponding  values  of 
V /\/C  and  then,  from  Table  IV,  the  corresponding  values  of  X 
and  the  other  elements. 

7.  Interpolate  between  the  values  thus  found  for  the  values 
corresponding  to  the  given  value  of  <£. 

Problem  1 1. — Assume  d  =  12  inches,         w  =  1046  Ibs. 
0  =  55°  40'  F  =  950f.  s. 

Determine  X,  T,  co,  and  v^. 

1.  d=w/d2  =  [Q. 86117] 

logV_    2.97772 

\ogV(\    0.43059 


logTV\/Ci     2.54713    V/VC\  =  352 . 48 

With  this  value  we  find  from  Table  IV,  for  0  =  56°, 

.25X156  =  3123 
3.49457 
logCi     0.86117 


log-X"!     4.35574    ^=22685  ft. 
=  7561.  7  yds. 

2.  From  the  table  of  values  of  c,  with  X  =  7562  yds.  and  <f>  =  56°, 
c  =  l.  79-.  562X0.  9  =  1.  739 


3.  C2  =  w/cld2  =  Cl/c1  =  [0.62087] 

For  use  in  Table  IV,  log_7    2.97772 

\ogVC  2    0.31044 


logF/\/C2    2.66728   7/N/Ca-464.81 
From  Table  IV,  for  0  =  56°, 

X/C2  =  4890  +  .  48  X 173  =  4973 

logAVCa    3.69662 

logC2    0.62087 

loX    4.31749 


408  ORDNANCE  AND  GUNNERY. 

log  (log  /)  =  log  X-  5 . 38029  5 . 38029 


log  (log/)     2.93720 


log/    0.08654 
logC2    0.62087 


logC3    0.70741 

Determine  F/VC3  log  V    2.97772 

0.35371 


2.62401    FAC  =  420. 74 


From  Table  IV,  for  <£  =  56°, 


X/C3  =  4213+  .07X168  =  4224.8 
logX/C3    3.62581 
log  C3    0.70741 


log.Y2    4.33322    X2  =  21539  ft. 
=  71 79.7  yds. 

4.  Since,  in  mortar  fire,  X  will  vary  but  little  for  a  variation  of 
one  degree  in  <£,  we  may  without  material  error  use  this  value  X2 
in  the  determination  of  c  for  55°  as  well  as  for  56°. 

Therefore,  from  the  table  of  values  of  c,  with  T  =  7180  yds.  and 

0  =  55°,  <£  =  56°, 

c2  =  1.77-.18X.12  =  1.748         c2  =  1. 79- .18X  .09  =  1.774 
C4=w/c2d2  =  C1/c2  =  [0. 61863]  C4  =  [0. 61222] 

5.  For  use  in  Table  IV, 

logF    2.97772  log  V    2.97772 

0.30932  log\/<^    0.30611 


logF/x/C4    2.66840  log  V/VC4    2.67161 

*  =  466 . 02  Vy\/C4  =  469 . 47 


EXTERIOR  BALLISTICS.  409 

From  Table  IV, 

X/C4  =  4959  +  .  6  X  176  =  5064  .  6  X/C4  =  5060  .  4 

log.Y/C4    3.70455  logX/C4  3.70418 

logC4    0.61863  logC4  0.61222 

log*    4.32318  log*  4.31640 

const.     5.40257  const.  5.38029 


log  (log/)    2.92061  log  (log  f)  2.93611 

log/    0.08329  log/  0.08632 

logC4    0.61863  logC4  0.61222 

logC5    0.70192  logC5  0.69854 

6.  For  use  in  Table  IV, 

log  V    2.97772  log  F  2.97772 

0.35096  logVC  0.34927 


logFA/C    2.62676  log  V/VC    2.62845 

3  =  425.06 


From  Table  IV, 

.34X170  =  4329.8 
.34X  .43  =  20.396 

.34X10'  =  59°  12'.4  ^=60° 

.34X7  =  363.38  vjVC 

From  the  above  values  we  derive 

X=21797  Z  =  21472 

T  =  45.763  T  =  46.272 


. 

,.-817.08 

7   Interpolating   between   these   values,    that    correspond   to 
,  =  55°  and  «#>  =  56°,  we  find  for  <£  =  550^ 

X  =  21580  ft.  =  7193  .  3  yards 
T  =  46  .  1  seconds 
w  =  59°46r.9 
t,  =  816.  5  foot  seconds 


410  ORDNANCE  AND  GUNNERY. 

It  will  be  seen  that  the  approximate  range,  X2  =  71  79.  7  yards, 
used  in  determining  the  value  of  c,  is  very  close  to  the  true  range, 
7193.3  yards. 

240.  Calculation  of  the  Coefficient  of  Reduction.  —  A  recent 
addition    to    Table   IV,    printed   in  the  Journal   of   the    United 
States  Artillery,  Jan.-Feb.,   1905,   provides  a  simple  method  of 
computing  the  coefficient  of  reduction  for  any  projectile,  when 
<f>}  V,  and  X  are  determined  from  actual  firings. 

A  column  containing  values  of  V2/X,  obtained  by  combining 
the  two  columns  V/Vc  and  X/C,  is  added  to  the  table.  With  <f> 
and  V2/X  as  arguments,  we  may  obtain  C  from  the  value  in  the 
column  F/v  C.  The  value  of  C  thus  obtained  is  the  complete 

value,  C  =  f-j;—fi.     Determine  /  from  the  formula  at  the  head  of 
1  d  cd2 

the  table,  and  3±/d  from  Table  VI.  c  is  then  readily  determined. 
When  the  additional  column  giving  the  values  of  V2/X  is  not 
at  hand,  the  value  of  F/Vc  corresponding  to  any  value  of  V2/X 
may  be  readily  determined  from  Table  IV  by  trial.  Square  the 
values  in  the  F/VC  column  and  divide  by  the  corresponding 
values  in  the  X/C  column  until  two  values  of  V2/X  are  found, 
one  value  greater  and  one  less  than  the  given  value.  By  inter- 
polation the  value  of  V/^/C  corresponding  to  the  given  value  of 
V2/X  may  then  be  found. 

241.  Problem  12.  —  The  range  of  the  1046  Ib.  projectile  from 
the  12  inch  steel  mortar,  model  1890  MI,  is  limited  to  11,215  yards. 
The  muzzle  velocity  of  the  projectile  is  1150  feet,  the  velocity 
being  limited  by  the  requirement  that  the  maximum  pressure 
shall  not  exceed  33,000  Ibs.     In  order  to  extend  the  range  of  the 
mortar  a  projectile  weighing  824  Ibs.  is  provided,  for  which,  with- 
out exceeding  the  allowed  pressure,  the  muzzle  velocity  is  in- 
creased to  1325  feet  and  the  range  to  12,713  yards. 

Compute  the  value  of  the  coefficient  of  reduction,  c,  for  that 
projectile  with  the  following  data  obtained  in  experiment. 


F  =  1325     <£  =  45°    .Y  =  38,139  feet 
Barometer,  30".  5  Thermometer,  65°  F. 

The  process  of  solution  is  indicated  as  follows: 


EXTERIOR  BALLISTICS.  411 

V*/X      Table  IV,  C  from  V/VC,      log  (log  /)  =  log  X-  const,  log. 


C=f-r 


From  the  given  data,  F2/Z  -  46 . 03 

From  Table  IV  we  find  with  this  value 

F/\/C  =  639.25 
logF    3.12222 
\ogV/Vc    2.80567 


logVC    0.31655 
logCc    0.63310 

log  (log  /)  =  log  X-  5 . 55099    log  X  4 . 58137 

const.  5.55099 


log  (log/)  1.03038 

log/  0.10725 

logV*  1.99211 

logw  2.91593 


3.01529 
log  Cd2    2 . 79146 


loge     0.22383  c  =  1.6743 

242.  Perforation  ol  Armor. — The  following  empirical  formulas 
are  used  by  the  Ordnance  Department,  U.  S.  Army,  for  calculating 
perforation  of  the  earlier  Krupp  armor. 

Uncapped  projectiles, 

7/)7)2 

^  =  [7.16459]-^ 

Capped  projectiles, 

w°'5v 
f°-r  =  [4. 84060]-^ 

tX 

in  which   t  =  thickness  perforated,  in  inches;  • 
w=  weight  of  projectile,  in  pounds; 
o  =  striking  velocity,  in  foot  seconds; 
d  =  diameter  of  projectile,  in  inches. 


412  ORDNANCE  AND  GUNNERY. 

The  following  formula  has  been  proposed  by  the  Ordnance 
Board  for  capped  projectiles  against  thin  plates: 


(-^—}      =[4.92665]^r^ 
V  sin  a.  I  J  d°'75 


in  which  a  is  the  angle  of  impact,  that  is  to  say,  the  angle  between 
the  axis  of  the  projectile  and  the  face  of  the  plate.  This  formula 
is  applicable  to  tempered  nickel  steel  plates  from  3  to  4|  inches 
thick,  and  for  angles  of  impact  varying  from  normal  to  50  degrees. 

The  following  formulas  are  used  by  the  Bureau  of  Ordnance, 
U.  S.  Navy,  for  calculating  the  perforation  of  face  hardened  armor 
without  backing.  They  apply  to  Harvey  armor  only.  No  for- 
mula satisfactory  to  the  Bureau  has  yet  been  developed  for  the 
perforation  of  the  most  modern  Krupp  armor. 

Uncapped  projectiles, 


v  =  [3. 34512]^ 
Capped  projectiles, 

v=[3. 


in  which  the  letters  represent  the  same  quantities  as  in  the  for- 
mulas above. 

The  formula  for  capped  projectiles  is  tentative  only. 

Range  Tables. — The  elements  of  the  trajectories  for  different 
ranges  are  calculated  for  each  gun  in  the  service  and  embodied 
with  other  information  in  a  range  table.  The  standard  muzzle 
velocity  and  standard  weight  of  projectile  are  used  in  the  con- 
struction of  the  table  for  each  gun.  The  range  is  the  argument  in 
the  table,  the  successive  entries  in  the  range  column  differing  from 
each  other  by  200  yards.  The  perforation  of  armor,  and  the 
logarithm  of  the  ballistic  coefficient  corrected  for  altitude  at  stand- 
ard temperature  and  pressure,  are  entered  at  intervals  of  1000 
yards. 

The  construction  of  range  tables  will  be  understood  from  the 
following  data  taken  from  the  first  line  of  the  range  table  for  the 
10-inch  rifle. 


EXTERIOR  BALLISTICS.  413 

Muzzk  Velocity,  2850  /.  s.          Projectile,  capped,  604  Ibs. 

RanSe>  x 1000  yards 

Angle  of  departure,  <j> 0°  34'. 1 

Change  in  elevation  for  10  yds.  in  range 0'.4 

Time  of  flight,  T 1.37  seconds 

Angle  of  fall,  a> .  0°  36' 

Slope  of  fall 1  on  95 

Maximum  ordinate,  y0 8  feet 

Striking  velocity,  v 2116  f.  s. 

Perforation  of  Krupp  armor,  impact  normal 13.3  inches 

"       "  30°  with  normal 11.2  inches 

Ballistic  coefficient,  log  C 0 . 78112 

Curvature  of  the  Earth.— The  angle  of  elevation  is  affected  by 
the  curvature  of  the  earth  about  15  seconds  of  arc  for  each  1000 
yards  of  range. 

The  amount  of  curvature,  in  feet,  is  approximately  two  thirds 
the  square  of  the  range  in  miles,  or 

Curvature  (ft.)  =  [7 . 33289]Z2(yds.)  (59) 

ACCURACY   AND   PROBABILITY  OF   FIRE. 

243.  Accuracy. — The  accuracy  of  a  gun  at  any  range  and  under 
any  given  conditions  of  loading  and  firing  is  determined  as  follows. 

A  number  of  shots  are  fired  under  the  given  conditions,  care 
being  exercised  to  make  the  circumstances  of  all  the  rounds  as 
nearly  alike  as  possible.  The  point  of  fall  of  each  shot  is  plotted 
on  a  chart  or  marked  on  the  target  when  practicable.  The  target 
may  be  either  horizontal  or  vertical.  We  will  assume  a  vertical 
target. 

The  coordinates  x  and  y  of  each  shot-mark,  or  impact,  are 
measured  with  respect  to  two  rectangular  axes  X  and  Y  drawn 
through  an  assumed  origin  conveniently  placed.  The  sum  of  the 
abscissas  divided  by  the  number  of  shots,  which  is  the  mean 
abscissa,  and  the  sum  of  the  ordinates  divided  by  the  same  num- 
ber, the  mean  ordinate,  are  the  coordinates  of  the  mean  point  of 
fall,  called  the  center  of  impact. 


414 


ORDNANCE  AND  GUNNERY. 


A  representation  of  a  target  of  8  shots  from  the  10-inch  rifle  is 
shown  in  Fig.  163.  The  range  was  3000  yards.  The  center  of 
impact  is  at  the  center  of  the  crossed  circle. 

The  distance,  in  the  direction  of  the  axis  of  Y,  of  any  impact 
from  the  center  of  impact  is  the  vertical  deviation  for  the  shot. 
The  deviation  is  plus  if  the  shot-mark  lies  above  the  center  of 
impact,  and  minus  if  below.  The  distance  of  the  shot-mark  from 
the  center  of  impact  in  the  direction  of  the  axis  of  X  is  the  lateral 
deviation  of  the  shot,  plus  if  to  the  right,  minus  if  to  the  left. 


ii — 


10  11  12  13 

FIG.  163. 

The  numerical  sum  of  the  horizontal  deviations  divided  by  the 
number  of  shots  is  the  mean  horizontal  deviation.  The  mean 
vertical  deviation  is  similarly  obtained  from  the  numerical  sum  of 
the  vertical  deviations. 

The  actual  distance  of  each  shot  from  the  center  of  impact  is 
the  absolute  deviation  for  the  shot,  and  the  mean  of  the  absolute 
deviations  is  the  mean  absolute  deviation  for  the  group. 

The  mean  absolute  deviation  is  usually  computed  from  the 
mean  horizontal  and  vertical  deviations  by  taking  the  square  root  of 
the  sum  of  their  squares.  The  value  computed  in  this  more  con- 
venient way  differs  slightly  from  the  mean  of  the  absolute  devia- 
tions. 

By  comparing  the  mean  absolute  deviations  of  different  groups 
of  shots  we  may  arrive  at  the  comparative  accuracy  of  different 
guns  or  of  the  same  gun  under  different  conditions  of  loading  or 
firing. 


EXTERIOR  BALLISTICS. 


415 


The  measure  of  the  ability  of  a  gunner  is  the  absolute  distance 
of  the  center  of  impact  of  the  group  of  shots  from  the  point  of  the 
target  aimed  at. 

244.  EXAMPLE.— In  a  test  of  the  10-inch  rifle  for  accuracy  8 
shots  were  fired  at  a  vertical  target  distant  3000  yards.  The  co- 
ordinates of  the  shots  measured  from  a  point  on  the  target,  see 
Fig.  163,  are  given  below.  Find  the  center  of  impact  and  the 
mean  absolute  deviation. 


Coordinates,  Feet. 

Deviations. 

No.  of 

Shot. 

Horizontal. 

Vertical. 

Horizontal. 

Vertical. 

1 

12.20 

11.00 

0.80 

1.65 

2 

11.50 

9.90 

0.10 

0.55 

3 

13.30 

9.75 

1.90 

0.40 

4 

11.70 

9.10 

0.30 

0.25 

5 

13.20 

9.15 

1.80 

0.20 

6 

9.00 

9.55 

2.40 

0.20 

7 

11.05 

7.15 

0.35 

2.20 

8 

9.25 

9.20 

2.15 

0.15 

8 

91.20 

74.80 

9.80 

5.60 

11.40 

9.35 

1.23 

0.70 

The  coordinates  of  the  center  of  impact  are:  horizontal,  11.40 
feet;  vertical,  9.35  feet. 

The  mean  deviations  from  the  center  of  impact  are:  horizontal, 
1.23  feet;  vertical,  0.70  feet. 

The  mean  absolute  deviation  =  -/E232+O702  =  1.42  feet. 

245.  Probability  of  Fire.* — Suppose  that  a  large  number  of 
shots  have  been  fired  at  a  target,  under  conditions  as  nearly  alike 
as  possible,  and  that  the  center  of  impact  of  the  group  of  shot- 
marks  on  the  target  has  been  determined. 

If  we  count  the  number  of  impacts  that  lie  within  any  given 
distance  from  the  center  of  impact  and  divide  this  number  by  the 

*  The  greater  part  of  the  discussion  of  the  subject  of  Probability  of  Fire 
follows  the  method  set  forth  by  Professor  Philip  R.  Alger,  U.  S.  Navy,  in  an 
article  appearing  in  the  Proceedings  of  the  U.  S.  Naval  Institute,  Whole  No.  108, 
1903,  and  in  the  Journal  of  the  United  States  Artillery,  March-April,  1904. 


416 


ORDNANCE  AND  GUNNERY. 


whole  number  of  shots,  the  resulting  fraction  will  express  the 
probability  that  any  shot  will  fall  within  the  given  distance. 

Probability  is  thus  always  expressed  as  a  fraction  of  unity.  If 
an  event  may  happen  in  a  ways  and 'may  fail  in  b  ways,  the  prob- 
ability of  its  happening  is  a/(a+b),  and  of  its  failing  to  happen, 
6/(a+6).  The  sum  of  these  two  fractions,  unity,  represents  the 
certainty  that  the  event  will  either  happen  or  fail.  Unity  there- 
fore indicates  certainty. 

By  examination  of  many  groups  of  shots  we  learn  that  as  we 
approach  the  center  of  impact  the  impacts  become  more  numerous, 
also  that  both  the  vertical  and  horizontal  deviations  are  as  likely 
to  be  on  one  side  of  the  center  of  impact  as  on  the  other. 

We  also  learn  that  the  vertical  and  horizontal  deviations  are 
entirely  independent  of  each  other,  and  that  any  vertical  deviation 
is  just  as  likely  to  occur  with  one  horizontal  deviation  as  with 
another.  This  makes  it  necessary  in  considering  probabilities 
that  we  consider  the  horizontal  and  vertical  deviations  separately. 

Let  0,  Fig.  164,  represent  the  center  of  impact  of  any  group  of 


o  a  b 

FIG.  164. 

shots  used  as  a  criterion.  Considering  only  lateral  deviations,  lay 
off  on  the  axis  of  X  successive  distances  representing  lateral  de- 
viations. 

Count  the  number  of  impacts  on  the  target  that  lie  within  the 
distance  Oa  to  the  right  of  the  center  of  impact.  Erect  at  a  an 
ordinate  of  such  length  that  the  area  of  the  rectangle  between  the 
ordinate  and  the  axis  of  Y  represents  the  number  of  impacts 
found  within  the  distance. 

Proceed  in  the  same  manner  for  the  distance  ab  and  for  the 
other  distances  represented  by  the  other  divisions  of  the  axis  of  X. 

The  area  of  any  rectangle  divided  by  the  area  of  all  the  rect- 
angles will  then  be  the  probability  that  any  shot  will  lie  within  the 


EXTERIOR  BALLISTICS.  417 

limits  of  deviation  between  the  limiting  ordinates.  As  the  total 
area  of  all  the  rectangles  is  a  constant,  the  probabilities  with  re- 
spect to  deviations  within  any  limits  represented  by  different  por- 
tions of  the  axis  of  X  are  proportional  to  the  rectangles  erected  on 
those  portions. 

246.  Probability  Curve. — If  we  consider  that  a  very  large 
number  of  shots  have  been  fired  and  make  the  rectangles  very 
small,  so  that  the  base  of  each  becomes  dx,  we  obtain  the  area  in 
the  figure  bounded  by  the  curve  and  the  axis  of  X. 

The  curve  is  called  the  probability  curve  and  the  area  under  any 
part  of  it  divided  by  the  whole  area  is  the  probability  that  any 
shot  will  deviate  from  the  center  of  impact  within  the  limits  be- 
tween the  limiting  ordinates. 

If  we  consider  the  whole  area  under  the  curve  as  unity,  the  area 
under  any  part  of  the  curve  will  represent  at  once  the  probability 
of  a  deviation  within  the  limits  between  the  limiting  ordinates. 

As  the  ordinates  may  be  considered  as  areas  infinitely  small  in 
width  any  ordinate  will  represent  the  probability  of  a  specific  devia- 
tion represented  by  the  abscissa;  that  is,  it  will  represent  the  proba- 
bility that  a  shot  will  fall  at  a  specific  distance  on  either  side  of 
the  center  of  impact.  The  area  of  the  ordinate  being  infinitely 
small  the  chance  that  a  shot  will  have  any  specific  deviation  is 
infinitesimal  and  not  worthy  of  consideration.  If  we  wrere  deal- 
ing with  events  that  could  happen  only  in  a  finite  number  of  ways, 
each  ordinate  would  be  an  area  that  would  have  a  finite  relation 
to  the  sum  of  all  the  ordinates  or  areas,  and  would  then  represent 
the  probability  of  the  happening  of  a  particular  event. 

CHARACTERISTICS. — The  curve  is  symmetrical  with  respect  to 
the  axis  of  Y,  since  the  probability  is  the  same  for  equal  deviations 
on  either  side.  The  ordinate  has  its  greatest  value  at  the  center  of 
impact,  since  the  center  of  impact  is  the  mean  position  of  all  the 
shots  and  the  probability  of  the  deviations  increases  continuously 
as  the  deviations  are  less.  The  curve  is  theoretically  an  asymptote 
to  the  axis  of  X,  since  all  deviations  between  +  oo  and  —  co  are 
possible.  Practically  it  may  be  considered  as  meeting  the  axis  of 
X  at  a  short  distance  from  the  center,  since  with  events  happening 
under  the  same  conditions  large  variations  from  the  mean  are  not 
to  be  expected. 


418  ORDNANCE  AND  GUNNERY. 

While  the  curve  as  deduced  applies  to  the  deviations,  or  errors, 
of  shot,  the  laws  that  are  expressed  by  it  are  general  in  character 
and  apply  to  accidental  errors  of  any  kind. 

247.  Equation  of  the  Probability  Curve. — The  equation  of 
the  curve  must  be  such  as  to  express  the  characteristics  just  enu- 
merated. Deduced  by  means  of  the  theory  of  accidental  errors, 
taking  as  its  basis  the  axiom  that  the  arithmetical  mean  of  observed 
values  of  any  quantity,  the  values  occurring  under  similar  circum- 
stances, is  the  most  probable  value  of  the  quantity,  the  equation 
takes  the  form 

y-^*-***  (6o> 

in  which  7-  is  the  mean  error,  in  our  case  the  mean  deviation,  and 
e  =  2.71828  the  base  of  the  Napierian  system  of  logarithms.  The 
factor  1/7:7-  is  introduced  to  make  the  whole  area  under  the  curve 

unity,  (  I        e~x*/*r*dx  =  7iY),    thus    obviating    the    necessity    of 

dividing  a  partial  area  by  the  whole  area  whenever  a  probability 
is  to  be  computed. 

As  stated  above,  the  area  under  any  part  of  the  curve  divided 
by  the  whole  area  under  the  curve  is  the  probability  that  the 
deviation  of  any  shot  will  lie  between  the  limits  of  deviation 
represented  by  the  part  of  the  axis  of  X  between  the  limiting  ordi- 

nates.    The  area  under  the  curve  is  f  ydx,  and   since  we  have 

introduced  into  y  in  equation  (60)  the  factor  required  to  make  the 
whole  area  unity,  the  integral  taken  between  limits  will  represent 
at  once  the  probability  for  any  limit  of  deviation. 

Thus  the  probability  that  any  shot  will  have  a  deviation  less 
than  the  numerical  value  Oa,  Fig.  164,  is 

P  =  2  fydx  =  —  fae-*2/«r2dx  (61) 

J  ~TJQ 

the  factor  2  appearing  since  the  ordinate  at  the  end  of  the  distance 
Oa  occurs  at  equal  distances  on  either. side  of  the  center. 

The  values  of  P  in  this  equation  for  various  values  of  a  and  ? 
are  arranged  in  the  following  table  with  a/f  as  an  argument. 
Knowing  the  mean  lateral  or  vertical  deviation  7-,  to  find  the  prob- 


EXTERIOR  BALLISTICS. 


419 


ability  of  a  shot  striking  within  the  distance  a  to  the  right  or  left 
of  the  center  of  impact,  it  is  only  necessary  to  take  from  the  table 
the  value  of  P  that  corresponds  to  the  argument  a/j-. 

PROBABILITY  OF  A  DEVIATION  LESS  THAN  a  IN  TERMS  OF    THE 

RATIO  a/- 


a 

r 

P 

a 
T 

P 

a 
T 

P 

a 

r 

P 

0.1 

0.064 

1.1 

0.620 

2.1 

0.906 

3.1 

0.987 

0.2 

0.127 

1.2 

0.662 

2.2 

0.921 

3.2 

0.990 

0.3 

0.189 

1.3 

0.700 

2.3 

0.934 

3.3 

0.992 

0.4 

0.250 

1.4 

0.735 

2.4 

0.945 

3.4. 

0.994 

0.5 

0.310 

1.5 

0.768 

2.5 

0.954 

3.5 

0.995 

0.6 

0.368 

1.6 

0.798 

2.6 

0.962 

3.6 

0.996 

0.7 

0.424 

1.7 

0.825 

2.7 

0.969 

3.7 

0.997 

0.8 

0.477 

1.8 

0.849 

2.8 

0.974 

3.8 

0.998 

0.9 

0.527 

1.9 

0.870 

2.9 

0.979 

3.9 

0.998 

1.0 

0.575 

2.0 

0.889 

3.0 

0.983 

4.0 

0.999 

248.  ILLUSTRATION  OF  THE  USE  OF  THE  TABLE. — On  December 
17,  1880,  at  Krupp's  proving  ground  at  Meppen,  50  shots  were 
'fired  from  a  12  cm.  siege  gun  at  5°  elevation,  giving  a  mean  range 
of  2894.3  meters.  The  points  of  fall  were  marked  on  the  ground 
and  their  distances  from  assumed  axes  measured.  The  center  of 
impact  was  thus  determined.  The  lateral  deviations  were  meas- 
ured from  the  center  of  impact.  The  mean  lateral  deviation  was 
1.07  meters. 

We  will  find  from  the  table  the  probability  that  any  shot  should 
have  a  deviation  of  less  than  one  meter  from  the  center  of  impact. 

The  deviation  is  a  =  l.  The  mean  lateral  deviation  is  ?-  =  1.07. 
Therefore  a/r  =  1/1 .07  =  0.935,  and  from  the  table,  P-0.544,  the 
probability  that  any  shot  will  fall  within  1  meter  of  the  center  of 
impact. 

For  50  shots  the  probability  is  that  PX50  shots  will  be  found 
within  this  limit  of  deviation,  P  X  50  =  0.544  X  50  =  27.  This  num- 
ber of  shots  actually  fell  within  the  limit  of  deviation  of  1  meter  in 
the  experiment. 

Making  a  =  2  meters,  n/r=  2/1.07  =  1.87,  P=  0.864,  and 
50X0.864  =  43.  The  probability  is  that  43  shots  out  of  the  50  will 
be  found  within  2  meters,  laterally,  of  the  center  of  impact. 
Forty-three  shots  were  actually  so  found. 


420  ORDNANCE  AND  GUNNERY. 

249.  Probable  Zones  and  Rectangles. — Since  P  is  the  prob- 
ability that  the  deviation  of  any  shot  will  not  be  greater  than  a, 
100P  represents  the  number  of  shots  in  100  that  will  probably  fall 
on  both  sides  of  the  mean  impact  within  the  limit  of  the  deviation 
a.  It  is  therefore  the  percentage  of  hits  that  will  probably  be 
found  in  the  zone  defined  by  the  limits  at  the  distance  a  in  both 
directions  from  the  center  of  impact.  From  the  table  we  find  that 
for  P  =  0.25,  or  100P  =  25  per  cent,  a/r  =  0.4,  or  a  =  0.4?-.  The 
half  width  of  the  zone  that  probably  contains  25  per  cent  of  hits 
is  therefore  0.4?-  and  the  full  width  of  the  zone  is  2a=0.8?-. 

This  zone  is  called  the  £5  per  cent  zone. 

Similarly  for  the  zone  that  probably  contains  50  per  cent  of 
hits,  the  50  per  cent  zone,  0  =  0.8467-  and  2a  =  1.69^. 

Knowing  the  mean  deviation,  vertical  or  horizontal,  we  may  at 
once  from  these  relations  find  the  width  of  either  zone. 

The  50  per  cent  zone  is  also  called  the  probable  zone  and  its 
half  width  is  the  probable  error,  or  deviation,  since  it  is  the  error 
that  is  just  as  likely  to  be  exceeded  as  not  to  be  exceeded. 

The  £5  per  cent  rectangle  is  the  rectangle  formed  by  the  inter- 
section of  the  50  per  cent  zones  for  lateral  and  vertical  deviations. 
The  probability  of  each  of  these  zones  being  1/2  the  probability 
of  the  rectangle  will  be  1/2X1/2. 

Similarly  the  50  per  cent  rectangle  is  that  formed  by  the  inter- 
section of  the  zones  for  each  of  which  P=v/l/2.  It  is  also  called 
the  probable  rectangle. 

COMPARISON  OF  THE  ACCURACY  OF  GUNS. — The  rectangles  of 
probability  may  be  used  in  comparing  the  accuracy  of  different 
guns.  The  probable  rectangle  is  generally  used  when  this  method 
is  employed. 

For  small  arms  and  high  powered  guns  using  direct  fire  the 
probable  rectangle  is  taken  hi  the  vertical  plane,  since  the  targets 
for  these  guns  usually  offer  a  vertical  front. 

For  guns  using  curved  or  high  angle  fire  the  probable  rectangle 
is  taken  in  the  horizontal  plane. 

Probability  of  Hitting  any  Area. — The  probability  of  hitting 
any  area  whose  width  is  2b  and  whose  height  is  2h,  and  which  is 
symmetrical  with  respect  to  the  center  of  impact,  as  the  area  abed, 
Fig.  165,  assuming  0  as  the  center  of  impact,  is  equal  to  the  product 


EXTERIOR   BALLISTICS. 


421 


of  the  two  values  o!  P  taken  from  the  table  with  b/Tx  and  h/rv  as 
arguments,  the  subscripts  indicating  lateral  and  vertical  deviations. 

If  the  center  of  impact  lies  in  the  7 

given  area,  or  on  its  edge,  the  proba- 
bility of  hitting  the  area  is  readily 
obtained  by. dividing  the  area  into  parts  <•,• 
by  lines  passing  through  the  center  of 
impact  and  taking  the  sum  of  the  prob- 
abilities of  hitting  the  parts. 

Thus  the  probability  of  hitting  the 
area  efgh,  Fig.   165,   is  the  sum  of  the  c 
probabilities  of  hitting  the  four  rect- 
angles into  which  it  is  divided  by  lines 
through    the    center  of   impact.      The 

probability  for  any  one  of  these  rectangles  is  1/4  the  probability 
for  the  area,  symmetrical  to  the  center  of  impact,  that  is  formed 
by  four  rectangles  equal  to  the  one  considered. 

If  the  center  of  impact  lies  wholly  without  the  area,  the  proba- 
bility of  hitting  the  area  is  obtained  by  extending  the  area  to 
include  the  center  of  impact  and  then  taking  the  difference  of  the 
probabilities  for  the  whole  area  and  for  the  part  added  to  the 
original  area. 

Thus  the  probability  for  the  rectangle  bg  is  equal  to  the  proba- 
bility for  the  rectangle  og  minus  the  sum  of  the  probabilities  for 
the  rectangles  ol  and  bk. 


FIG.  1G5. 


APPENDIX  TO  CHAPTER  IX. 
THE    USE   OF  TABLE  II—  INGALLS'  BALLISTIC  TABLES. 

250.  Description  of  Table  II. — The  several  functions  in  this 
table  are  functions  of  two  independent  variables,  V  and  Z.  Each 
function  varies  with  V  and  Z  according  to  the  law  expressed  by 
the  equation  which  gives  the  value  of  the  function,  and  the  several 
functions  vary  differently.  Thus  the  functions  A  and  A'  and 
others  decrease  as  V  increases  and  increase  as  Z  increases  through- 
out the  table.  The  functions  A"  and  log  E'  increase  with  V  and 


422  ORDXANCE  AXD  GUNNERY. 

increase  with  Z  up  to  a  value  of  7  =  2500,  beyond  which  point 
they  will  be  found  to  increase  with  V  for  certain  values  of  Z  and 
to  decrease  with  V  for  other  values  of  Z.  The  function  u  in- 
creases with  V  and  decreases  with  Z  throughout  the  table. 

The  values  of  any  function  given  in  the  table  are  the  computed 
values  obtained  by  assuming  successive  values  for  V  and  Z  in  the 
equation  of  the  function.  The  constant  difference  100  is  taken 
between  the  successive  values  of  Z.  As  most  of  the  functions  vary 
more  rapidly  when  V  is  small,  the  computed  values  are  taken 
close  together  for  the  lower  values  of  V  and  at  greater  intervals 
for  the  larger  values  of  V.  Thus  for  values  of  V  below  1000  the 
computations  were  made  for  values  of  V  differing  from  each  other 
by  25.  Between  7  =  1000  and  7  =  2000,  the  difference  between 
the  tabular  values  of  7  is  50,  and  above  7  =  2000  the  difference  is 
100.  The  purpose  of  this  course  was  to  obtain  in  the  tables  cor- 
rect values  of  the  functions  so  close  to  each  other  as  to  permit  the 
assumption,  without  material  error,  that  the  function  varies  uni- 
formly between  the  tabulated  values.  This  assumption  enables  us 
to  interpolate  between  the  given  values  with  comparative  ease. 

251.  Deduction  of  Formulas  for  Double  Interpolation.— To 
obtain  a  formula  for  interpolation  we  will  proceed  as  follows.  A 
function  of  two  independent  variables  may  be  graphically  repre- 
sented by  the  length  of  a  line  drawn  perpendicular  to  the  plane 
which  contains  the  axes  of  the  variables.  The  variables  in  the 
tables  are  7  and  Z.  Let  us  take  from  the  table  a  value  of  any  one 
of  the  functions,  as  A,  and  call  this  value  /0,  the  corresponding 
values  of  7  and  Z  being  called  70  and  Z0.  Let  the  axis  of  7  be 
horizontal  and  the  axis  of  Z  vertical.  From  the  point  7oZ0  on 
the  plane,  Fig.  166,  draw  a  line  perpendicular  to  the  plane,  and 
lay  off  on  it  the  length  /0  equal  to  the  value  of  the  function  taken 
from  the  table.  Lay  off  the  distance  ZoZ2  parallel  to  the  axis  of 
Z  and  equal  to  100.  From  Z2  draw  a  line  perpendicular  to  the 
plane  and  lay  off  on  it  the  value  of  the  function  given  in  the  same 
table  for  the  next  greater  value  of  Z.  Lay  off  7072  parallel  to 
the  axis  of  7  and  equal  to  the  difference  between  the  two  velocities 
given  in  the  caption  of  the  table,  and  call  this  distance  h.  On  a 
perpendicular  to  the  plane  at  72  lay  off  the  value  of  the  function 
taken  from  the  next  succeeding  table  for  the  first  value  of  Z,  and 


423 

from  a  point  at  a  distance  of  100  below  F2  lay  off  the  next  suc- 
ceeding value  of  the  function  from  this  table.  Complete  the  figure 
shown  by  the  heavy  lines.  The  solid  represented  by  this  figure  is 
made  up  of  all  the  values  of  the  function  lying  between  the  four 
tabular  values. 


FIG.  166. 

Let  us  cut  the  solid  by  a  plane  through  V  in  the  figure  at  a 
distance  V—  V0  from  V0,  and  by  another  plane  through  Z  in  the 
figure  at  a  distance  Z—Zo  from  Z0.  The  intersection  of  these  two 
planes,  /,  will  be  the  value  of  the  function  corresponding  to  the 
values  V  and  Z.  In  the  column  marked  Az  in  the  table,  opposite 
the  value  of  each  function,  appears  the  difference  between  this 


424  ORDNANCE  AND  GUNNERY. 

value  and  the  value  next  below.  This  difference  for  /0,  called 
AZQ,  is  represented  in  the  figure;  and  similarly  the  corresponding 
difference  in  the  Av  column,  which  is  the  difference  between  the 
values  of  the  function  for  the  same  value  of  Z  and  successive 
tabular  values  of  V,  is  shown  as  AvQ  in  the  figure;  and  the  next 
succeeding  difference  in  the  same  column  is  shown  as  Av\  at  the 
bottom  of  the  figure.  Draw  vertical  lines  from  c,  m,  and  I. 
From  the  figure: 

/o—  dc+ab=f 

V-V0 
h:Jv0::V—V0:dc  dc  =  —  r 

From  the  triangle  cnm  we  have: 

lQQ:nm::Z-Z0:ab 

Z-Zp 

ao  =  nm 


V-V0 
ml  =  —  7  —  Avi 

—  JZ0—  (Ai\  —  Jv0) 


V-Vo.     ,Z-Z0\ 
Mo- 


The  above  expression  having  been  deduced  under  the  condi- 
tions that  the  function  decreases  with  V  and  increases  with  Z,  we 
will  indicate  this  by  writing  /["J1  for  /.  Transposing  the  terms 
of  this  formula,  for  convenience,  it  may  be  written  : 

Z-Z0.       V-Vo         Z-Z0  V-V0 


EXTERIOR  BALLISTICS.  425 

v 

and  by  changing  the  signs  according  to  the  manner  of  the  variation 
of  the  function  with  V  and  Z,  we  may  write  the  formulas  for  those 
functions  that  vary  in  a  different  manner. 

The  formula  gives  the  value  of  the  function  corresponding  to 
the  values  of  V  and  Z  between  the  tabular  values.     If  we  solve  it 
for  V  we  obtain  an  expression  for  the  value  of  V  when  non-tabular 
values  of  the  function  and  of  Z  are  given;  and  similarly,   solving 
it  for  Z,  the  resulting  formula  will  give  the  value  of  Z  correspond- 
ing to  non-tabular  values  of  the  function  and  of  V. 
The  formulas  will  be  of  the  form  given  below. 
252.  Double  Interpolation  Formulas  —  Ballistic  Table  II. 
/  =  non-tabular  value  of  any  function  corresponding  to  the  non- 

tabular  values  V  and  Z. 
/o  =  tabular  value  of  function  corresponding  to  tabular  values  V0 

and  ZQ,  always  the  nearest  values  less  than  V  and  Z. 
h  =  difference  between  velocities  given  in  caption  of  table. 
AVQ  and  Jzo  =  tabular  differences  for  /0. 
Jvi  =  tabular  difference  next  following  Jr0  in  same  table. 

indicates  that  function  decreases  as  V  increases  and  increases 

as  Z  increases. 

Use  the  following  formulas  for  the  functions  A,  A',  B,  T,  log 
C",  and  D'  throughout  the  table.  They  also  apply  for  some  values 
of  the  functions  A"  and  log  Bf  when  V  >  2500. 


1 


Use  the  following  formulas  for  the  functions  A"  and  log  E' 
when  F<2500,  and  for  some  values  beyond  that  point. 


426  ORDNANCE  AND  GUNNERY. 

Z-Z0       ,  F-Fo,        Z-Z0  F 


F=FO+' 


v_v 


xioo 


Use  the  following  formulas  for  the  function  u. 

Z-Z0       ,  F-Fo,       Z-Z0  V-V0 


XIOO 


k 


Inspect  the  tables  to  determine  how  the  function  varies  with 
V  and  Z,  and  select  the  proper  group  of  formulas. 

Exercise  great  care  in  the  use  of  the  plus  and  minus  signs. 

Double  Interpolation  in  Simple  Tables. — Regarding  Fig.  166, 
from  which  the  above  formulas  have  been  deduced,  we  will  see  that 
the  interpolated  value  /  of  the  function  may  be  obtained  from  the 
four  tabular  values  represented  by  the  four  heavy  corner  lines  of 
the  figure.  Interpolating  by  the  rule  of  proportional  parts  be- 
tween the  value  /0  of  the  function  and  the  value  immediately 
below  it  in  the  same  table  for  F,  which  value  is  represented  at  Z2 
in  the  figure,  we  obtain  the  value  of  the  function  at  V0Z  in  the 
figure.  Proceeding  in  the  same  manner  in  the  table  for  the  next 
value  of  F  we  obtain  the  value  of  the  function  at  V2Z  in  the  figure. 


EXTERIOR  BALLISTICS.  427 

Interpolating  between  the  values  at  V0Z  and  V2Z  we  obtain  the 
desired  value  /. 

This  method  is  the  most  convenient  method  of  double  inter- 
polation in  simple  tables,  such  as  Table  VI  of  the  Ballistic  Tables. 
The  numbers  in  that  table  are  simple  and  the  data  is  all  found 
together  on  one  page. 

USE   OF  THE   FORMULAS. 

253.  Given  Non-Tabular  Values  of  V  and  Z,  to  Find  f.— 

Select  the  /  formula  applicable  to  the  particular  function.  Take 
from  the  table  the  value  of  the  function  corresponding  to  the 
tabular  values  of  V  and  Z  next  less  than  the  given  values.  The 
tabular  values  of  V  and  Z  are  V0  and  Z0  in  the  formula.  Express 

~IT y  y y 

the  fractions  -        -  and  -       -  decimally.     If  we  take  from  the 

fl  1UU 

table  at  the  same  time  with  the  function  the  corresponding  num- 
bers in  the  Az  and  Av  columns,  also  the  number  next  following  in 
the  Av  column,  called  respectively  AzQ,  AvQ,  and  Ai\  in  the  formula, 
we  have  all  the  data  necessary  for  the  solution  of  the  problem. 
The  numbers  in  the  different  columns  of  the  table  are  obtained 
by  considering  the  values  of  the  functions  as  whole  numbers. 
The  corrections  therefore  must  be  applied  to  the  function  as  if  it 
were  a  whole  number. 

In  the  examples  which  follow  we  will  indicate  by  enclosing  the 
decimal  values  of  functions  in  parentheses  that  they  are  to  be  con- 
sidered as  whole  numbers  in  applying  the  corrections. 

EXAMPLE. 
1.  Given  V  =  1015        Z  =  374.2        What  is  the  value  of  A'? 

FT7  1  -  *7         *7 

-KO    lo  Z— Z0  , 


Jz0  =  96        AVQ = 223         Ai\  =  230 

/  =  (0.2946)  +  .42  X  96  -  .3  X  223  -  .42  X  .3  X  7 
=  (0.2946)  +  40.32  -  66.9  -  .88 
=  (0.2946) -27.5 
=0.29185 


428  ORDNANCE  AND  GUNNERY. 

2.  Given  V  =  887        Z  =  7Z75        What  is  the  value  of  log  Bf? 


h         25  100 

/  =  (0.09779)  +  .75  X  133  +  .48  X  59  -  .75  X  .48  X  1  =  0.099067 

To  help  in  fixing  the  formulas  for  /  in  the  mind,  we  will  note 
that  the  correction  for  Az  is  applied  with  a  positive  sign  if  the  func- 
tion increases  with  Z,  and  with  a  negative  sign  if  the  function 
decreases  with  Z.  The  correction  for  An  is  similarly  applied  ac- 
cording as  the  function  varies  with  V.  The  sign  of  the  last  term 
is  positive  if  the  signs  of  the  two  preceding  terms  are  similar,  and 
negative  if  they  are  dissimilar.  The  difference  between  the  two 
values  of  Av  in  the  last  term  is  usually  positive  and  no  attention 
need  be  paid  to  the  sign  of  this  difference  except  when  dealing 
with  the  functions  log  B'  and  log  C". 

The  formulas  used  in  the  above  examples,  which  we  will  call 
the  /  formulas,  and  which  give  the  values  of  the  functions  for  non- 
tabular  values  of  V  and  Z,  indicate  the  simplest  and  quickest 
method  of  arriving  at  the  correct  value  of  an  interpolated  func- 
tion. This  method  should  therefore  always  be  followed  in  solving 
problems  of  this  nature. 

3.  Given  V  =  1630  Z  =  3781  Find  D'  Ans.  155.9 

4.  Given  V  =  972.  4  Z  =  9569  Find  A  Ans.  0.464181 

5.  Given  V  =  2790  Z  =  1255  Find  log  C'  Ans.  4.65946 

6.  Given  V  =  2790  Z  =  8473  Find  log  C'  Ans.  4.97732 

Note  the  difference  in  the  signs  of  the  last  term  of  the  formula 
in  the  two  preceding  examples;  also  the  sign  of  the  same  term  in 
the  following  example. 

7.  Given  7  =  1217      Z  =  8778      Find  log  B'     Ans.  0.138514 
Note  that  in  the  following  example  A"  decreases  with  V. 

8.  Given  V  =  3040      Z  =  4926      Find  A"  Ans.  2952.4 

254.  Given  Non-Tabular  Values  of  the  Function  and  of  V, 
to  Find  Z.  —  Select  the  Z  formula  applicable  to  the  particular 
function.  Inspect  the  table  on  the  page  that  contains  the  given 
value  of  V  to  find  the  proper  values  to  substitute  in  the  formula 


EXTERIOR  BALLISTICS.  429 

for  /o,  Z0}  and  the  tabular  differences.  To  arrive  at  accurate  re- 
sults this  requires  some  little  care,  and  is  best  done  in  the  following 
manner.  By  rapid  inspection  of  the  table  find  the  two  values  of 
the  function  between  which  the  given  value  lies.  Apply  to  the 
tabular  value  corresponding  to  the  larger  value  of  Z  the  correc- 

V-VQ 
tion  —  T  —  4v0.     By  comparing  the  corrected  tabular  value  with 

the  given  value  we  determine  on  which  side  of  the  corrected 
tabular  value  the  given  value  lies,  and  thereby  determine  which 
value  of  Z  to  use  for  /0  and  the  differences  in  the  formula.  An 
example  will  illustrate  this. 

9.  Given  A  =  0.06121        V  =  2192        Find  Z. 


. 

h 

Looking  in  the  table  for  F  =  2100  we  find  that  the  given  value 
of  A  lies  between  the  values  corresponding  to  Z  =  5100  and 
Z  =  5200.  Applying  to  the  value  of  the  function  corresponding  to 

V-V0 
the  larger  value  of  Z  the  correction  —  7  —  Ji?0  =  .  92X571  =  525 

we  have  (0.06263)  -525  =0.05738  as  the  value  of  the  function  for 
T  =  2192  and  Z  =  5200.  This  value  is  less  than  the  given  value  by 
about  380,  and  as  the  function  increases  with  Z  the  given  value 
lies  below  it  in  the  table. 

The  tabular  Az  for  the  value  of  the  function,  0.06263,  that  we 
have  taken  from  the  table,  is  about  190;  that  is  the  function  is  here 
increasing  by  about  190  for  each  tabular  value  of  Z.  The  tabular 
function  when  corrected  gave  us  a  value  too  small  by  380.  Con- 
sequently if  we  take  the  second  value  of  Z  greater  than  5200,  the 
one  we  have  used,  we  shall  probably  have  the  value  we  seek. 

We  will  therefore  take  the  function  for  Z  =  5400  and  apply  the 
correction  to  get  its  value  for  F  =  2192.  The  corrected  value  is 
(0.06639)  -.92X602  =0.060852.  As  this  is  less  than  the  given 
value  of  A  and  close  to  it,  we  know  that  the  given  value  lies 
between  £  =  5400  and  Z  =  5500,  and  we  will  use  Z  =  5400  and  the 
corresponding  tabular  values  in  the  formula. 

It  will  be  observed  in  each  of  the  formulas  for  Z  and  V  that, 
in  the  numerator  of  the  last  term,  there  is  a  term  in  parentheses 


430  ORDNANCE  AND  GUNNERY. 

containing  /0  plus  or  minus  a  correction.  This  term  in  paren- 
theses is  the  tabular  value  of  the  function  corrected  for  the  differ- 
ence between  the  given  value  of  V  or  Z  and  the  next  less  tabular 
value.  It  is  essential,  in  order  to  arrive  at  correct  results,  that  the 
value  of  this  term  be  found  first;  for,  as  shown  above,  it  is  only  by 
this  means  that  we  can  determine  the  true  tabular  values  of  Z  or 
V  between  which  the  required  value  lies.  It  will  be  shown  later 
that  without  these  values  correct  results  cannot  be  obtained. 

In  this  example  we  have  found  the  value  of  the  term  in  paren- 
theses to  be  (0.06639)  -.92X602  =  0.060852.  Using  this  in  the 
formula  with  the  given  value  of  the  function  and  the  tabular 
quantities  corresponding  to  /o,  the  process  becomes  exceedingly 
simple,  and  the  required  value  is  easily  and  quickly  and  accu- 
rately obtained. 

Z0  =  5400    /o  =  0.06639 
6121-  6085.2 


OKQ 

Z  =5400  +     olOO  =  5420.1 


If  we  had  not  pursued  the  above  course,  but  had  used  for  Z0 
the  smaller  value  of  Z  obtained  at  our  first  inspection  of  the  table, 
the  result  would  have  been  as  follows. 


The  difference  in  the  results  is  due  to  the  fact  that  in  using 
the  value  Z  =  5100  we  assume  that  the  function  varies  uniformly 
between  this  value  and  the  obtained  value,  a  difference  of  332, 
while  our  process  of  interpolation  is  based  on  the  assumption  that 
the  variation  is  uniform  for  a  difference  in  Z  of  100  only. 

The  effect  of  the  difference  in  the  values  of  Z  obtained  by  the 
two  methods  may  be  seen  in  the  problem  from  which  the  above 
data  were  taken.  The  value  of  the  ballistic  coefficient,  C,  was 
4.7859  and  the  range  X  was  required.  X  =  ZC. 

With  Z  =  5420.1  X  =  25940  ft. 

With  Z  =  5432.6  X  =  26000  ft. 


EXTERIOR  BALLISTICS.  431 

It  may  sometimes  be  more  convenient,  after  having  found  the 
proper  value  of  Z  for  use  in  the  formula,  to  obtain  from  the  table 
the  corrected  values  of  the  function  for  that  value  of  Z  and  for 
the  next  greater  value  of  Z.  The  given  value  of  the  function  will 
lie  between  these  two  corrected  tabular  values,  and  the  true  value 
of  Z  may  be  found  by  the  method  of  proportional  parts. 

For  V  =  2192     Z  =  5400     A  =  (0.06639)  -  .92  X  602  =  0.060852 
Z  =  5500     A  =  (0.06832)  -  .92  X  618  =  0.062634 

1782 
A,  given,  .06121 

.060852 


0X0 

£  =  5400+^100  =  5420.1 

The  results  given  by  the  two  methods  are  the  same.  Indeed 
the  methods  are  the  same,  for  through  the  agency  of  4z0  and  Ji^ 
in  the  formula  we  make  use  of  the  tabular  values  of  the  function 
corresponding  to  the  second  value  of  Z.  It  will  be  seen  in  the 
examples  above  that  the  fractions  to  be  reduced  are  exactly  alike. 

In  problems  in  the  text  books  on  exterior  ballistics  the  value 
of  Z  is  nearly  always  determined  to  the  nearest  tenth.  This  in- 
dicates that  it  is  important  to  obtain  the  correct  value.  The 
correct  value  can  be  obtained,  from  the  tables,  only  by  inter- 
polating between  the  nearest  tabular  values  on  each  side.  The 
importance  of  the  preliminary  application  of  the  correction 

V-V0 
— T — 4v0  to  the  tabular  values  of  the  function,  for  the  purpose  of 

determining  the  proper  value  of  Z  to  use,  is  therefore  apparent. 

In  using  the  formulas  for  Z  and  V  the  fractional  coefficients 
of  100  and  of  h  in  the  last  terms  will  always  inform  us  whether  we 
are  in  the  proper  place  in  the  tables.  Both  numerator  and 
denominator  of  the  fraction  must  be  positive,  and  the 
value  of  the  fraction  must  be  less  than  unity.  A  negative 
value  of  the  fraction  or  a  value  greater  than  unity  indicates  that 
we  have  not  used  the  nearest  values  of  /0  and  V0  or  Z0  and  the 
differences.  The  result  is  therefore  approximate  only,  and  the 


432  ORDNANCE  AND  GUNNERY. 

degree  of  approximation  varies  with  the  number  of  units  in  the 
value  of  the  fraction. 

The  formulas  for  V  and  Z  may  be  easily  fixed  in  the  memory 
if  we  observe  that  the  numerator  of  the  .last  term  is  the  difference 
between  the  given  value  of  the  function  and  the  nearest  corrected 
tabular  value,  the  correction  being  applied  to  the  tabular  value 
with  a  sign  indicated  by  the  manner  of  variation  of  the  function 
with  Z  or  V.  The  first  term  of  the  denominator  is  AvQ  in  the  V 
formulas,  and  Az$  in  the  Z  formulas.  The  sign  of  the  second  term 
of  the  denominator  is  the  same  as  the  sign  inside  the  parentheses 
of  the  numerator.  The  value  of  the  second  term  of  the  denomi- 
nator is  positive  for  all  the  functions  except  log  B'  and  log  C'.  For 
some  value  of  log  B',  and  for  most  values  of  log  Cf,  Ji\  is  less 
than  Jv0,  so  that  (Av\  —  Jr0)  becomes  negative  and  causes  a  change 
of  sign  for  the  second  term  of  the  denominator  in  the  V  and  Z 
formulas,  and  for  the  last  term  in  the  /  formulas. 

10.  Given  u  =  991         V  =  1630        Find  Z. 

F-70_30 
h         50 

This  value  of  u  apparently  lies  between  the  values  of  Z  =  4600 

V-V0 
and  Z  =  4700,  but  applying  the  correction  —  7  —  Jvo  =  .6Xl5  =  9 

to  987,  the  tabular  value  of  the  function  for  Z  =  4700,  adding  it 
since  u  increases  with  V,  we  find  that  the  value  of  u  for  F  =  1630 
and  Z  =  4700  is  996.  This  being  greater  than  our  given  value, 
and  the  function  decreasing  with  Z,  the  given  value  corresponds 
to  a  value  of  Z  greater  than  4700.  Similar  inspection  shows  that 
the  proper  value  of  Z  is  less  than  4800.  We  therefore  use  the 
values  for  Z  =  4700  in  the  formula. 

/0  =  987  Jz0  =  6     Ju0  =  15     M  =  15 

QQA_ 


o  +  U 

11.  Given  A"  =2158        V  '  =  979        Find  Z. 
V-V0 


h 


=  .16 


EXTERIOR  BALLISTICS.  433 

The  change  in  the  function  here  is  very  slight  for  a  change  in 
7,  and  we  see  at  once  that  this  value  of  A"  lies  between  Z  =  4000 
and  Z  =  4100. 


12.  Given  B  =  0.0341  7  =  2763  Find  Z  Ans.  4053.4 

13.  Given  D' =  790  7  =  1784.6  Find  Z  A ns.  7278.1 

14.  Given  log  B'  =0.07140  7  =  1146  Find  Z  Ans.  3894.9 

15.  Given  A' =  0.2252  7  =  970  Find  Z  Ans.  2813.1 

255.  Given  Non-Tabular  Values  of  the  Function  and  of  Z, 
to  Find  V. — This  problem  is  slightly  more  troublesome  than  the 
one  just  explained,  because  as  7  is  not  given  we  cannot  turn 
directly  to  the  page  on  which  the  nearest  tabular  value  of  the 
function  will  be  found. 

Select  the  7  formula  applicable  to  the  particular  function. 
With  the  next  tabular  value  of  Z  less  than  the  given  value  look 
through  the  table  until  two  consecutive  tables  are  found  which, 
for  this  value  of  Z,  give  values  of  the  function  less  and  greater 

<7 >7 

than  the  given  value.     Apply  the  correction  °Jz0  to  the 

tabular  value  corresponding  to  the  larger  value  of  7  and  deter- 
mine, from  the  corrected  tabular  value,  the  side  on  which  the 
given  value  lies,  and  the  proper  table  to  use. 

16.  Given  B =0.32386        Z  =  5887        FindV. 

Z-Z0 


100 


=  .87 


Inspecting  the  tables  with  the  value  Z  =  5800  we  find  that 
tabular  values  of  the  function  greater  and  less  than  the  given 
value  are  found  in  the  consecutive  tables  for  7  =  900  and  7  =  925, 
these  values  being  respectively  0.3388  and  0.3230.  Apparently 
then  the  value  of  7  for  the  given  function  lies  between  900  and 
925,  and  the  values  for  /0,  70,  etc.,  in  the  formula,  should  be  taken 
from  the  table  for  7  =  900.  But  applying  the  correction 

>7 >7 

—Az0  =  . 87X77  =  67  to  the  tabular  value  of  the  function  for 
£  =  5800  and  7  =  925,  adding  it  since  B  increases  with  Z,  we  obtain 


434  ORDNANCE  AND  GUNNERY. 

for  the  function  at  7  =  925  and  Z  =  5887,  the  value  0.3297,  which 
is  greater  than  the  given  value.  Since  B  decreases  with  V  the 
given  value  must  therefore  lie  to  the  right  of  the  value  for  V  =  925, 
and  as  the  difference  between  the  two  is  considerably  less  than 
the  Ju  in  the  table,  144,  we  know  without  further  inspection  that 
the  value  for  V  lies  between  925  and  950,  and  in  the  formula  we 
will  use  the  quantities  taken  from  the  table  for  7  =  925. 

70  =  925          Z0=5SOO  /o  =  0.3230 


In  a  manner  similar  to  that  explained  in  the  first  problem  under 
the  previous  heading  this  same  value  of  V  can  be  obtained,  after 
having  found  the  value  of  the  function  for  Z=5887  and  V  =  925,  by 
finding  the  value  of  the  function  corresponding  to  Z  =  5887  and 
the  next  tabular  value  of  V,  950,  and  determining  the  true  value 
of  V  by  the  method  of  proportional  parts. 

For  Z  =  5887         V  =  925         B  =  (0.3230)  +  .87  X  77  =  0.3297 
V  =  950         B  =  (0.3086)  +  .87  X  74  =0.31504 


1466 
3297 
B,  given,  32386 


584 

25  =  935 


17.  Given  T'  =  9.130        Z  =  9378        Find  V. 

Z-Z0 


100 


'  =  .78 


Inspecting  the  table  with  Z  =  9300,  we  find  that  the  given 
value  of  T"  lies  between  the  tabular  values  for  7  =  1600  and 
7  =  1650.  Adding  to  9.046,  the  value  of  T'  for  the  larger  value  of  7, 
the  correction  .78  X 128,  we  find  that  T'  for  Z  =  9378  is  9.146.  We 
know  then  that  the  value  of  7  sought  is  greater  than  1650;  and 
since  9.146-9.130  is  less  than  the  Av  in  the  table,  152,  we  know 


EXTERIOR  BALLISTICS.  435 

that   V  lies  between  1650  and  1700.     We  therefore  use  in  the 
formula  the  values  from  the  table  for  7  =  1650. 


18.  Given  log  E'  =  0.1652        Z  =  4G2J        Find  V. 


__ 

100 

From  the  value  of  tan  a>,  equation  (35),  we  have  B/=— 

tan  (j> 

The  same  range  may  be  attained  by  different  shots  fired  with 
different  velocities  at  different  angles  of  elevation.  The  angles  of 
fall  will  also  be  different.  But  the  changes  in  the  angle  of  eleva- 
tion and  angle  of  fall  may  be  such  that  the  ratio  of  the  tangents  of 
the  angles  wall  remain  constant.  We  may  therefore  get  similar 
values  for  B',  and  for  its  logarithm,  with  one  value  of  A'  and  widely 
different  values  of  V.  When,  therefore,  log  B'  is  given  and  a 
value  of  Z,  since  Z  contains  A"  as  a  factor,  we  may  find  in  the 
tables  more  than  one  value  of  V  corresponding  to  these  given 
values.  Should  this  case  be  encountered  in  the  solution  of  a 
ballistic  problem,  the  proper  value  of  V  to  use  would  be  deter- 
mined after  consideration  of  the  other  data  of  the  problem. 

With  the  data  given  above  we  find  the  two  following  solutions, 
in  the  tables  for  7  =  1900  and  7  =  2900  respectively;  using  in  the 
first  the  formula  for  7  when  log  &  corresponds  to  a  value  of 
7  <  2500,  and  in  the  second  the  formula  for  7  when  log  B'  corre- 
sponds to  a  value  of  7  >  2500. 

17  _  <7 

log  £'=0.1652    Z  =  4625 


As  we  have  before  noted,  the  functions  A"  and  log  B',  for  some 
values  of  Z,  increase  with  7  when  7  <  2500  and  decrease  with  7 
beyond  that  point.  Therefore  we  may  expect  to  find,  for  these 


436  ORDNANCE  AXD  GUNXERY. 

values  of  Z,  equal  values  of  either  function  on  both  sides  of 
7  =  2500. 

19.  Given  w  =  931. 3  Z  =  8122.7    Find  V    Am.  2187.5 

20.  Given  B =0.16801          Z  =  6345       Find  V    Ans.  1832.0 

21.  Given  Tr  =  3. 7943          Z  =  4852        Find  V    Ans.  1747.0 

22.  Given  log  B'  =  0.23376  Z  =  7318       Find  7    Ans.  2226.0 

256.  Given  One  Function  and  V  or  Z,  to  Find  the  Corre- 
sponding Value  of  Another  Function. — Inspecting  the  formulas 
for  V  and  Z  we  see  that  'the  fractional  coefficients  of  h  and  100, 

V— V  Z—Z 

in  the  last  terms,  are  respectively  equal  to  -         -   and  - 

fl  1UU 

We  therefore  take  out  this  coefficient  from  the  Z  formula  if  V  is 
given  with  the  function,  and  from  the  V  formula  if  Z  is  given, 
using  the  formula  applicable  to  the  given  function.  Substitute 

17 y  77 Y 

the  value  thus  obtained  for  —r-.  -  or  for  — r —  in  the  /  formula 

100  n 

applicable  to  the  required  function,  using  for  /0  and  the  differ- 
ences in  this  formula  the  tabular  values  for  the  required  function 
corresponding  to  the  same  values  of  V  and  Z  as  were  used  in  the 
previous  operation. 

23.  Given  A"  =  3 150     V  =  1929.5    Findu. 

V-V0 


h 


=  .59 


From  the  Z  formula  for  A"  when  F<2500 

5200 

Z-Z0  =  3150- (3116  +  5.9)  _ 
100  65 +  .59 

It  will  always  be  well  when  taking  from  the  table  the  quanti- 
ties required  in  computing  the  coefficient  (Z— Z0)/100  from  the  Z 
formula  to  write  above  Z0  the  tabular  value  used,  as  it  is  written 
in  the  above  equation.  This  will  serve  as  a  memorandum  as  to 
what  value  of  Z0  to  use  when  computing  the  value  of  the  required 
function. 

The  memorandum  is  not  necessary  when  computing  (V—  V0)/h, 
as  the  value  of  V0  is  indicated  on  the  page  at  which  the  table  is 
open. 


EXTERIOR  BALLISTICS.  437 

Substituting  the  value  of  this  coefficient,  obtained  above,  in 
the  /  formula  for  the  function  w,  and  using  for  /0  and  the  differ- 
ences in  this  formula  the  tabular  quantities  for  the  function  u  for 
the  same  values  of  V  and  Z  used  in  computing  the  coefficient, 

u  =  1041  -.43X8+.  59X14-  0  =  1045.8 

24.  Given  Dr  =  125     V  =  3018    Find  A". 

V-Vo_ 
h 

5500 

tf~\v  7)        • — —  — • — • • — •   A / 

100          7-. 18 

Since  V  is  greater  than  2500  we  must  inspect  the  table  to  see 
how  A"  varies  for  the  value  of  Z  used.  We  find  that  A"  is  here 
diminishing  with  V  and  increasing  with  Z.  The  first  of  the  / 
formulas  is  therefore  appropriate. 

A"  =  3364+.  67X73-.  18X6-0  =  3411.8 

25.  Given  A'  =  0.0401    Z  =  540    Find  Tr. 


100 

For  Z  =  500  this  value  of  A'  lies  between  the  values  given  for 
T  =  900  and  7  =  925.  Applying  the  correction  for  Z  to  the  value 
corresponding  to  F  =  925,  we  find  that  925  is  the  proper  value  of 
V  to  use  in  the  formula. 

V-Vo     418-401 
"F"  =  19  +  4X.4~ 

T  =  (0.548)  +  .4X  111-.  825X  14-.  4X.  825X3  =0.5799 
26    Given  log  B'  =  0.0809    Z  =  ®565    Find  log  Cf. 


00 

F-Fo    809-786.65 
for  log  B      -jp    -44+2X.65~ 

logC'  =  (5.3076)  +  .65X34-.493X274-.65X.493X2  = 
27    Given  A'  =  0.2485  F  =  2180.4    Find  B          Ans.  0.15578 

28*  Given  r  =  7.698  Z  =  5728       Find  Df         Ans.  1013.3 

29!  Given  log  B'  =  0.1832     V  =  1832       Find  u  Ans.  954.2 

30.  Given  A  =  0.01669          Z  =  1224.5    Find  log  C"    Ans.  5.1347 


CHAPTER  X. 


PROJECTILES. 

257.  Classification. — Projectiles  are  classed  as  shot,  shell,  and 
case  shot.  The  shell  is  a  hollow  shot  designed  to  be  filled  with  a 
bursting  charge  that  by  means  of  a  fuse  may  be  exploded  at  a 
selected  time.  The  case  shot  consists  of  a  number  of  shot  held 
together  by  an  enclosing  envelope  which  may  be  ruptured  by  the 
shock  of  discharge  or  by  a  bursting  charge  in  flight.  The  en- 
velopes of  canister  and  grape  shot  are  ruptured  by  shock  in  the 
gun.  The  envelope  of  shrapnel  is  ruptured  by  a  bursting  charge. 

Old  Forms  of  Projectiles. — In  the  old  smooth  bore  cannon 
round  cast  iron  shot  and  shell  of  diameter  nearly  equal  to  the  caliber 
of  the  gun  were  used.  The  grape,  canister,  and  shrapnel  for  these 


(I 


i 


GRAPE. 


CANISTER. 


guns  are  shown  in  the  illustrations.  The  shrapnel  was  invented 
about  1803  by  Colonel  Shrapnel  of  the  British  Army.  In  its  first 
form  it  contained  a  number  of  lead  balls  with  loose  powder  in  the 
interstices.  The  walls  of  the  shell  were  made  thick  to  resist  def- 
ormation by  the  movement  of  the  contained  balls.  In  its  later 
forms  the  spaces  between  the  balls  were  filled  with  melted  sulphur, 

438 


PROJECTILES. 


439 


and  a  chamber  for  the  bursting  charge  was  provided  as  shown. 
By  this  arrangement  the  walls  were  no  longer  subject  to  the  im- 
pact from  the  loose  balls,  and  therefore  could  be  made  thinner, 


SHRAPNEL. 

thus  providing  room  for  a  greater  number  of  bullets.  The  con- 
fining of  the  bursting  charge  in  a  chamber  made  its  explosive  effect 
greater  and  permitted  a  reduction  in  its  weight. 

Chain  shot  and  bar  shot,  made  up  of  two  projectiles  connected 
by  a  chain  or  bar,  were  occasionally  used  in  early  times;  and  in- 


STUDDED.  EUREKA.  BUTLER. 

cendiary  shell,  called  carcasses,  which  were  ordinary  shell  filled 
with  combustible  material,  the  flames  from  which  issued  through 
holes  drilled  through  the  walls  of  the  shell. 

Smooth  bore  guns  were  succeeded  by  muzzle  loading  rifled 
guns  The  introduction  of  rifling  brought  about  the  use  of  elon- 
gated projectiles  of  increased  weight.  The  capacity  of  the  gun  in 
weight  of  metal  thrown  was  largely  increased  and  much  greater 
accuracy  of  fire  was  obtained. 


440 


ORDNANCE  AND  GUNNERY. 


For  the  projectiles  for  the  muzzle  loading  rifled  cannon  some 
device  was  necessary  to  cause  the  projectile  to  take  the  rifling. 
The  several  devices  that  were  employed  are  shown  in  the  illustra- 
tions on  the  preceding  page. 

The  studs  on  the  projectile  shown  in  the  first  figure  were  fitted 
into  the  grooves  of  the  rifling  as  the  projectile  was  inserted  at  the 
muzzle.  In  the  other  projectiles  shown  the  parts  a  are  of  brass, 
and  in  firing  were  expanded  outward  into  the  rifling  by  the  pres- 
sure of  the  powder  gases.  Other  means  that  were  employed  are 
shown  hi  Figs.  167,  168,  and  169. 


FIG.   168. 


FIG.  169. 


Fig.  167  shows  the  Hotchkiss  projectile.  The  parts  a  and  b 
are  of  iron  and  are  held  apart  by  the  ring  of  lead  c.  The  gas  pres- 
sure acting  on  the  part  b  forced  the  lead  outward  into  the  rifling. 

Fig.  168  shows  the  Whitworth  projectile.  The  bore  of  the 
"Whitworth  gun  was  a  twisted  prism  of  hexagonal  cross  section  as 
shown  in  Fig.  169.  The  projectile  was  fashioned  to  fit  the  bore, 
its  sides  being  provided  with  surfaces  of  a  similar  prism. 

258.  Modern  Projectiles.  BANDING. — With  the  introduction 
of  breech  loading  in  arms  of  all  kinds  the  problem  of  giving  rota- 
tion to  the  projectile  was  much  simplified  As  the  chamber  of 
the  gun  is  larger  than  the  bore,  a  projectile  provided  with  a  soft 
metal  band,  b  Fig.  170,  of  diameter  larger  than  the  diameter  of 
the  bore,  may  be  inserted  through  the  chamber.  On  the  explosion 
of  the  charge  the  pressure  causes  the  sloping  ends  d  of  the  lands 
of  the  rifling  to  force  their  way  through  the  rotating  band,  causing 
the  band  to  conform  in  shape  to  the  section  of  the  rifling,  and 


PROJECTILES. 


441 


assuring  the  proper  rotation  in  the  projectile.  As  the  band  com- 
pletely fills  the  cross  section  of  the  bore  it  serves  also  as  a  check 
to  prevent  the  escape  of  gas  past  the  projectile,  and  in  addition  it 


a 


FIG,   170. 

serves  to  center  the  projectile  in  the  bore,  and  to  determine  a 
fixed  position  of  the  projectile  when  rammed  into  the  gun. 

The  banding  of  projectiles  is  practically  the  same  for  all  cali- 
bers. An  undercut  groove,  b  Fig.  171,  is  cut  around  the  projec- 
tile near  the  base.  A  straight  band  of 
copper,  of  cross  section  a»>  shown  at  a,  is 
hammered  into  the  groove  and  com- 
pletely fills  it,  as  shown  at  e.  The  ends 
of  the  band  are  beveled  lengthwise  and 
make  a  scarf  joint  where  they  .meet.  The 
bands  for  projectiles  of  small  caliber  are 
solid  rings  of  metal  forced  into  the  grooves 
of  the  projectile  under  hydraulic  pressure. 
The  bottom  of  the  groove  6  is  scored  with 
vertical  cuts  into  which  the  copper  enters 
when  the  band  is  hammered  on.  These 

prevent  the  rotation  of  the  band  independently  of  the  projectile. 
The  width  of  the  band  depends  upon  the  caliber  of  the  projectile 
and  is  greater  for  the  larger  calibers.  The  outer  surface  of  the 
band  is  smooth  in  projectiles  for  siege  and  smaller  caliber  guns. 
In  the  wider  bands  of  the  larger  projectiles  a  number  of  grooves  are 
cut,  as  shown  in  section  at  e,  Fig.  170,  to  diminish  the  resistance  to 


FlG   171 


442 


ORDNANCE  AND  GUNNERY. 


forcing  and  to  provide  space  for  the  metal  forced  aside  by  the 
lands  of  the  rifling. 

In  the  latest  6-inch  wire  wound  guns,  in  which  velocities  of  over 
3400  feet  have  been  produced,  difficulty  has  been  experienced  on 
account  of  the  tendency  of  the  jointed  rotating  bands  to  strip 
from  the  projectile  during  flight,  due  to  the  effect  of  the  centrif- 
ugal force.  A  band  made  by  winding  a  thin  copper  ribbon  on 
edge  and  filling  the  groove  has  been  tried  with  these  projectiles 
but  without  success. 

It  is  probable  that  the  method  of  banding  with  solid  rings 
seated  by  hydraulic  pressure  will  ultimately  be  used  with  these  and 
with  larger  projectiles. 

259.  FORM  OF  PROJECTILE. — With  the  exception  of  the  can- 
ister all  modern  projectiles  are  of  the  same  general  shape,  a  cylin- 
drical body  with  ogival  head.  The  ogival  head  is  found  by  ex- 
periment to  be  the  most  advantageous,  as  it  offers  little  resistance 
to  the  air  and  at  the  same  time  provides  enough  metal  at  the  point 
of  the  projectile  to  give  to  the  point  the  requisite  strength  to  per- 
form the  work  of  penetration. 

The  ogive  is  struck  from  a  center  on  a  line  perpendicular  to  the 
axis  of  the  projectile,  Fig.  172,  and  with  a  radius  usually  ex- 


BODY 

; 

0 

i                   LJ 

- 

?  Q 

_l 

CO 

<< 

\                  LJ 

CD 

• 

1                g 

I              CD 

_  

__ 

AXIS.  

.  -4-—  I  



I 

I 

1 

II 
II 

II 
II 
II 

II 


FIG.  172. 


pressed  in  calibers.     The  radius  of  the  head  varies  in  different 
projectiles  from  \\  to  3  calibers. 

The  lower  part  of  the  ogive  is  turned  off  to  make  a  cylindrical 
bearing  surface  for  the  front  part  of  the  projectile.     This  surface, 


PROJECTILES. 


443 


a     o 


called  the  bourrekt,  has  a  diameter  1/100  of  an  inch  less  than  the 
diameter  of  the  gun. 

Below  the  bourrelet  the  diameter  of  the  projectile  is  diminished, 
for  ease  of  manufacture  and  to  prevent  bearing  in  the  gun,  to 
about  7/100  of  an  inch  less  than  the  caliber.  The  band  is  placed 
from  1£  to  2J  inches  from  the  base,  depending  on  the  caliber,  the 
greatest  diameter  of  the  band  exceeding  the  caliber  by  from  1/10 
to  3/10  of  an  inch. 

The  length  of  projectile  varies  between  1\  and  5  calibers.  The 
length  of  most  of  the  seacoast  projectiles  is  3^  calibers. 

Canister. — Canister  projectiles  are  for  use  at  very  short  range, 
when  the  guns  of  a  battery  are  being  charged  by  the  enemy.  The 
projectile  consists  of  a  number  of  small  balls 
contained  in  a  metallic  envelope  so  con- 
structed that  it  will  break  into  pieces  at  the 
shock  of  discharge.  In  our  service,  canister 
are  provided  for  the  mountain  guns  only. 
The  canister  for  the  75  m|m  Vickers  Maxim 
gun  is  shown  in  Fig.  173. 

The  case,  c,  made  of  malleable  iron,  is  solid 
at  the  bottom  and  open  at  the  top.  It  is 
weakened  by  two  series  of  cuts,  s,  each  series 
consisting  of  three  oblique  cuts,  each  of  which 
extends  over  an  arc  of  120  degrees.  The  case 
contains  244  iron  balls  f  of  an  inch  in  diameter 
and  weighing  30  to  the  pound.  The  balls  are 
confined  in  the  case  by  the  tin  cup,  a,  riveted 
in.  Three  holes,  h,  drilled  through  the  bottom 
of  the  case  admit  the  powder  gases  to  assist 
in  rupturing  the  case.  The  metallic  cartridge 
case  is  attached  to  the  projectile  by  being 
crimped  at  several  points  into  the  groove  r. 
The  copper  band,  6,  forms  a  stop  for  the 
head  of  the  cartridge  case,  and  serves  as  a  FIG.  "173. 

gas  check  in  the  gun.  The  groove  g,  in  other  projectiles,  is  filled 
with  grease  for  the  purpose  of  preventing  the  entrance  of  moisture 
into  the  cartridge  case. 

It  is  the  present  intention  of  the  Ordnance  Department  not  to 


444  ORDNANCE  AND  GUNNERY. 

manufacture  any  more  canister.  Their  place  will  be  taken  by 
shrapnel,  which  are  so  constructed  that  they  may  be  burst  within 
25  feet  of  the  muzzle  of  the  gun. 

260.  Shrapnel. — The  modern  shrapnel  is  a  projectile  designed 
to  carry  a  number  of  bullets  to  a  distance  from  the  gun  and  there 
to  discharge  them  with  increased  energy  over  an  extended  area. 
It  is  particularly  efficacious  against  troops  in  masses  and  is  not 
used  against  material.  The  shrapnel  is  the  principal  field  artillery 
projectile.  It  is  also  provided  for  mountain  and  siege  artillery 
and  for  use  in  the  small  caliber  guns  in  seacoast  fortifications  in 
repelling  land  attacks. 

In  the  earlier  models  the  case  of  the  shrapnel  was  so  con- 
structed as  to  break  into  a  number  of  fragments  on  explosion  of 
the  bursting  charge,  with  the  idea  of  thus  practically  increasing 
the  number  of  bullets  carried.  With  the  same  end  in  view  the 
spaces  between  the  balls  were  filled  with  the  parts  of  cast  metal 
diaphragms  that  separated  the  layers  of  balls  and  broke  up  into 
additional  fragments  at  the  bursting  of  the  projectile.  The 
bursting  charge  was  placed  sometimes  in  the  head  and  sometimes 
in  the  base  of  the  projectile.  It  was  found  with  these  shrapnel 
that  a  very  large  percentage  of  the  numerous  fragments  had  not 
sufficient  energy  to  inflict  serious  injury.  The  shrapnel  is  there- 
fore at  present  constructed  of  a  stout  case  which,  except  for  the 
blowing  out  of  the  head,  remains  intact  at  the  explosion  of  the 
bursting  charge,  and  from  which  the  balls  are  expelled  in  a  forward 
direction  and  with  increased  velocity  by  the  bursting  charge  in 
the  base.  By  these  means,  while  the  number  of  fragments  is 
less,  a  greater  number  possess  the  required  energy  and  the 
effective  range  of  these  is  increased. 

Fig.  174  represents  the  shrapnel  for  the  3-inch  field  gun. 
The  case,  c,  is  a  steel  tube  drawn  in  one  piece  with  a  solid 
base.  A  steel  diaphragm,  d,  rests  on  a  shoulder  near  the  base, 
forming  a  chamber  for  the  bursting  charge  in  the  base  of  the 
projectile,  and  a  support  for  a  central  steel  tube  which  extends 
through  the  head,  h.  A  small  quantity  of  guncotton  in  the 
bottom  of  the  tube  is  ignited  by  the  flame  from  the  fuse,  and 
in  turn  ignites  the  bursting  charge.  The  balls,  of  lead  hardened 
with  antimony,  are  252  in  number.  Each  ball  is  49/100  of  an 


PROJECTILES. 


445 


—c 


inch  in  diameter  and  weighs  approximately  167  grains,  or  42  to 

the  pound.     After  the  balls  are  inserted  a  matrix  of  mono-nitro- 

naphthalene  is  poured  into  the  case,   filling 

the  interstices  between  the  balls  in  the  lower 

half  of  the  case.     When  cool  this  substance 

is  a  waxy  solid.     It  gives  off  a  dense  black 

smoke  in  burning.    The  purpose  of   its  in- 
troduction  is    to   render   the  burst  of    the 

shrapnel  visible  from   the  gun  so  that  the 

gun  commander  may  determine  whether  his 

projectiles  are  attaining   the   desired  range. 

Resin  is  used  as  the  matrix  in  the  forward 

half  of  the  case. 

The  matrix  forms  a  solid  mass  with  the 

balls  and  prevents  their  deformation  by  the 

pressure  that  they  would  exert  upon  each 

other,  on  the  shock  of  discharge  in  the  gun, 

if  they  were  loose  in  the  case.    Resin  gives 

better  support  to  the  balls  than  naphthalene 

and  therefore  no  more  of  the  naphthalene  is 

used  than  is  necessary  to  produce  the  desired  / 

amount  of  smoke. 

On    being   expelled   from    the   case   the 

matrix   burns  and   breaks   up,  leaving   the 

balls  free. 

To  prevent  rotation  of  the  contained  mass  in  the  case  the  interior 

•of  the  case  is  fluted  lengthwise,  so  that  its  cross  section  is  as  shown 
in  Fig.  175;  and  to  reduce  the  friction  to  a 
minimum,  particularly  in  the  chamber  for  the 
bursting  charge,  the  interior  of  the  case  is  coated 
with  a  smooth  asphalt  lacquer. 

The  head,  h,  of  steel  is  given  a  cellular  form 
to  make  it  as  light  as  possible.  The  weight  of 
the  projectile  complete  is  fixed  at  15  Ibs.,  and 
weight  is  saved  as  far  as  possible  in  all  parts  of 

the  case  in  order  that  the  greatest  number  of  balls  may  be  carried. 

The  head  is  screwed  into  the  body  and  fixed  by  two  brass  pins,  p. 

The  combination  time  and  percussion  fuse,  /,  is  screwed  into  the 


-  -d 


FIG.  174. 


FIG.  175. 


446  ORDNANCE  AND  GUNNERY. 

head.  It  is  protected  against  injury  or  tampering  by  the  spun 
brass  cap,  6,  soldered  on  to  the  head  of  the  projectile. 

The  projectile  is  fixed  in  the  cartridge  case  as  explained  for  the 
canister. 

Shrapnel  forms  80  per  cent  of  the  ammunition  supply  of  the 
field  gun. 

261.  The  Bursting  of  Shrapnel. — When  the  shrapnel  bursts 
the  balls  are  expelled  forward  with  increased  velocity,  and  as  they 
have  at  the  same  time  the  movement  of  rotation  of  the  projectile 
they  are  dispersed  more  or  less  to  the  right  and  left.  Their  paths 
form  a  cone,  called  the  cone  of  dispersion,  about  the  prolongation 
of  the  trajectory.  The  section  of  this  cone  at  the  ground  is  an 
irregular  oval  with  its  longer  axis  in  the  plane  of  fire.  The  dimen- 
sions of  the  area  will  vary,  as  is  evident  from  Fig.  176,  with  the 


FIG.  176. 

angle  of  fall,  the  height  of  burst,  and  the  relation  between  the 
velocities  of  translation  and  rotation  at  the  moment  of  burst. 

It  is  assumed  that  when  a  shrapnel  ball  has  an  energy  of  58  foot 
pounds  it  has  sufficient  force  to  disable  a  man,  and  with  287  foot 
pounds  of  energy  it  will  disable  a  horse.  These  energies  corre- 
spond in  the  service  shrapnel  bullet  to  velocities  of  about  400  and 
880  foot  seconds.  An  increased  velocity  of  from  250  to  300  feet  is 
imparted  to  the  balls  by  the  bursting  charge.  Knowing  the  ve- 
locity of  the  projectile  and  the  weight  of  the  balls  the  space  within 
which  the  balls  will  be  effective  may  be  determined  for  any  range. 

POINT  OF  BURST. — The  best  point  of  burst  for  a  shrapnel  is 
assumed  to  be  that  point  from  which  the  burst  of  the  shrapnel  will 
produce  practically  one  hit  per  square  yard  of  vertical  surface  at 
the  target.  It  is  determined  from  the  cone  of  dispersion  by  find- 
ing the  right  section  that  contains  as  many  square  yards  as  there 
are  bullets  in  the  shrapnel.  The  distance  in  front  of  the  target 
at  which  the  burst  occurs  is  called  the  interval  of  burst.  On  ao- 


PROJECTILES. 


447 


count  of  the  variation  at  different  ranges  in  the  velocities  of  trans- 
lation and  of  rotation  the  interval  of  burst  which  will  produce  one 
hit  per  square  yard  of  vertical  surface  at  the  target  varies  with 
the  range,  decreasing  as  the  range  increases. 

Practically  it  is  found  best  to  consider  the  height  of  burst 
rather  than  the  interval  of  burst,  since  the  battery  commander  can 
more  readily  estimate  the  height  than  the  interval.  Suitable 
cross  hairs  in  the  field  of  the  battery  commander's  telescope  facili- 
tate this  estimation. 

In  our  service  a  height  of  3/1000  of  the  range,  called  3  mils,  is 
adopted  as  the  most  favorable  mean  height  of  burst.  The  point 
of  burst  at  this  height  gives,  over  a  large  part  of  the  range,  very 
approximately  the  correct  interval  of  burst.  For  short  ranges 
this  height  of  burst  is  excessive,  and  for  long  ranges  it  is  insuffi- 
cient. 

The  following  table  shows  for  the  3-inch  shrapnel  the  results 
obtained  at  different  ranges  from  bursts  at  the  correct  interval  of 
burst,  and  also  at  a  height  of  burst  of  3  mils.  The  front  of  target 
that  should  be  covered  depends  upon  the  number  of  balls  in  the 
shrapnel  For  the  3-inch  shrapnel  with  270  bullets,  a  former 
model,  the  front  to  be  covered  with  one  hit  per  square  yard  is  18.5 
yards. 


One  Hit  per  Square  Yard. 

Height  of  Burst,  3  Mils. 

Range. 

Interval. 

Front  Covered. 

Interval. 

Front  Covered. 

Yards. 

Yards. 

Yards. 

Yards. 

Yards. 

1000 

81.4 

18.5 

11S.J 

27.0 

2000 

73.0 

18.5 

83.4 

21.2 

2500 

68.98 

18.5 

73.5 

19.55 

3000 

65.84 

18.5 

66.6 

18.76 

3500 

63.28 

18.5 

60.9 

18.84 

4000 

61.07 

18.5 

56.4 

17.12 

4500 

58.97 

18.5 

51.3 

16.13 

It  will  be  observed  that  between  2000  and  4500  yards  the 
height  of  burst  of  3  mils  gives  approximately  the  desired  density 
of  fire  at  the  target.  At  ranges  less  than  2000  yards  the  front 
covered  is  largely  increased  and  the  density  of  fire  therefore  dimin- 
ished. 

The  figures  refer  to  a  single  shrapnel  bursting  at  the  mean 


448  ORDNANCE  AND  GUNNERY. 

point  of  burst.  In  a  group  of  shrapnel  the  bursts  above  and  below 
the  mean  point  would  largely  make  up  the  discrepancies  in  dis- 
tribution and  density. 

FUSE. — The  fuse  used  in  the  shrapnel  is  the  combination  time 
and  percussion  fuse  of  which  a  full  description  will  be  found  in  the 
chapter  on  fuses.  The  fuse  is  arranged  in  such  a  manner  that  if 
the  projectile  is  not  burst  in  flight  it  will  be  burst  soon  after  im- 
pact, a  short  time  being  allowed  by  the  delay  element  in  the  fuse, 
during  which  the  projectile  may  rise  on  a  graze  and  its  burst  be 
accomplished  in  the  air. 

The  fuse  is  also  constructed  to  permit  of  using  the  shrapnel  as 
canister.  When  the  fuse  is  set  at  zero  of  the  time  scale,  the  pro- 
jectile will  burst  within  25  feet  of  the  muzzle  of  the  gun. 

262.  Shot  and  Shell. — Solid  shot  are  no  longer  used  in  modern 
cannon  except  for  target  practice,  at  least  in  our  service.  Certain 
hollow  projectiles  with  thick  walls  designed  principally  for  the 
perforation  of  armor  are  denominated  shot  to  distinguish  them 
from  shell,  which  name  is  given  to  thinner  walled  projectiles  that 
have  not  as  great  a  penetrative  power  but  carry  larger  bursting 
charges,  and  have  consequently  greater  destructive  effect  after 
penetration. 

Shell  were  formerly  made  of  cast  iron,  being  cast  in  one  piece 
and  subsequently  bored  for  the  fuse,  Fig.  177. 


FIG.  177. 

With  the  adoption  of  high  explosives  for  bursting  charges, 
greater  strength  in  the  walls  of  shell  became  desirable  in  order  to 
insure  against  accidental  explosion  of  the  projectile  while  in  the 
gun.  With  the  exception  of  some  of  the  projectiles  for  guns  of 
minor  caliber  in  which  black  powder  is  used  for  the  bursting  charge, 
all  projectiles  are  now  made  of  forged  steel. 

Fig.  178  represents  a  steel  shell  for  the  5-inch  siege  rifle.  The 
steel  projectiles  for  mountain,  field  and  siege  artillery  are  similarly 
constructed. 


PROJECTILES. 


449 


The  base  of  the  shell  is  closed  by  a  steel  base  plug,  p,  wliich  is 
screwed  in  after  the  explosive  charge  has  been  packed  in  the  pro- 
jectile. The  plug  is  bored  and  tapped  for  the  base  fuse,  /,  wliich 
when  inserted  is  flush  with  the  rear  surface  of  the  projectile.  The 
wrench  holes  in  base  plug  and  in  head  of  fuse  are  filled  with  lead  hi 
order  to  make  a  continuous  bearing  surface  for  the  copper  cup,  c. 
The  cup  is  applied  to  the  base  of  the  shell  to  prevent  the  powder 
gases  in  the  gun  from  penetrating  to  the  interior  of  the  projectile 
by  way  of  the  joints  of  the  screw  threads.  The  edge  of  the  cup 


-S 


FIG.  178. 

fits  into  the  circular  undercut  groove,  g,  and  the  joint  there  is 
sealed  and  the  cup  held  in  place  by  lead  wire  hammered  in. 

Armor  Piercing  Projectiles.— Armor  piercing  projectiles  are  of 
the  same  general  construction  as  the  steel  shell  just  described. 
Their  distinguishing  feature  is  a  soft  metal  cap  embracing  the 
point  of  the  projectile  for  the  purpose  of  increasing  the  power  of 
the  projectile  in  the  perforation  of  hard  armor. 

The  head  and  point  of  an  armor  piercing  projectile  are  ex- 
tremely hard,  the  hardness  being  attained  in  the  process  of  manu- 
facture by  any  one  of  several  secret  tempering  processes.  The 
metal  of  the  projectile  before  being  subjected  to  the  secret  process 
has  a  tensile  strength  of  about  85,000  pounds  per  square  inch, 
which  is  undoubtedly  increased  by  the  tempering.  The  cap,  on  the 
other  hand,  has  a  tensile  strength  not  exceeding  60,000  pounds,  with 
a  large  percentage  of  elongation,  and  reduction  of  area,  as  may  be 
seen  in  the  table  on  page  165.  The  metal  of  the  cap  is  therefore 
very  soft  compared  with  the  metal  in  the  head  of  the  projectile. 

A  10-inch  armor  piercing  shot  is  shown  in  Fig.  179  and  a  10- 
inch  shell  in  Fig.  180. 

The  shot  has  thicker  walls  and  head,  and  a  less  capacity  for 


450 


ORDNANCE  AND  GUNNERY. 


FIG.  179. 
10-in.  Armor  Piercing  Shot. 


FIG.  180. 
10-in.  Armor  Piercing  Shell. 


PROJECTILES. 


451 


the  bursting  charge.  The  outer  diameters  of  the  two  projectiles 
are  the  same,  and  the  weight  of  each  when  ready  for  firing  is  the 
same,  604  pounds.  To  maintain  uniformity  of  weight  the  shot  is 
made  about  4|  inches  shorter  than  the  shell. 

The  cap  is  fixed  to  the  head  of  the  projectile  by  means  of  the 
circular  groove,  a,  cut  around  the  head  of  the  projectile.  The  cap 
before  affixing  is  of  the  shape  shown  half  in  section  and  half  in 
elevation  in  the  figure  between  the  projectiles.  A  shallow  recess, 
6,  is  filled  with  graphite  to  lubricate  the  projectile  as  it  passes 
through  the  cap  and  armor.  To  fasten  the  cap,  the  projectile  with 
the  cap  on  its  point  is  put  in  a  lathe,  and  the  excess  metal  at  the 
base  of  the  cap  is  hammered  into  the  groove  of  the  projectile  by 
means  of  pneumatic  hammers. 

In  naval  projectiles  the  caps  are  sometimes  fastened  on  by 
passing  two  wires  through  holes  drilled  in  the  cap  and  notches  cut 
in  the  projectile. 

263.  Action  of  the  Cap. — The  soft  steel  cap  increases  the 
power  of  penetration  to  the  projectile  in  hard  faced  armor,  at 


FIG.  181. 

normal  impact  and  up  to  an  angle  of  30  degrees  from  the  normal, 
about  15  per  cent  with  respect  to  the  velocity  of  the  projectile 
and  more  than  20  per  cent  with  respect  to  the  thickness  of  plate. 

Among  the  several  theories  advanced  as  to  the  action  of  the 
cap,  the  following  appears  the  most  satisfactory. 

When  an  uncapped  projectile  strikes  the  extremely  hard  face 
of  a  modern  armor  plate,  the  whole  energy  of  the  projectile  is 
applied  at  the  point,  and  the  high  resistance  of  the  face  of  the 
plate  puts  upon  the  very  small  area  at  the  point  of  the  projectile  a 


452 


ORDXAXCE  AXD   GUXXERY. 


stress  greater  than  the  metal  can  resist,  however  highly  tempered 
it  may  be.  The  point  is  therefore  broken  or  crushed  and  the  head 
of  the  projectile  flattened,  Fig.  181.  The  flattening  of  the  head 
brings  loss  of  penetrative  power,  and  the  energy  of  the  projectile 
is  expended  largely  in  shattering  the  projectile  itself.  The  head 
of  the  projectile  adheres  to  the  plate  and  is  practically  welded 
to  it. 

The  effect  on  a  plate  of  thickness  equal  to  the  caliber  of  the 
projectile  may  be  the  partial  or  complete  punching  out  of  a  cylin- 
drical piece,  Fig.  182.  But  even  if  the  plate 
is  completely  perforated,  the  projectile  does 
not  get  through  as  a  whole;  and  behind  the 
plate  are  found  only  fragments  of  the  pro- 
jectile and  of  the  metal  forced  from  the 
plate. 

When  a  projectile  provided  with  a  cap 

strikes  a  hard  faced  plate,  the  pressure  due  to  the  resistance  of  the 
plate  is  not  confined  simply  to  the  point  of  the  projectile,  but  is 
distributed  uniformly  over  a  comparatively  large  cross  section.  In 


FIG.   182. 


FIG.   183. 


addition  the  point  of  the  projectile  is  firmly  supported  on  all  sides 
by  the  metal  of  the  cap.  As  a  consequence  the  point  is  not  de- 
formed, and  passing  easily  through  the  cap  it  finds  the  hard  face 


PROJECTILES. 


453 


of  the  plate  dished  and  severely  strained  and  more  or  less  crum- 
bled by  the  impact  of  the  cap.  The  unexpended  energy  of  the 
projectile  forces  the  point  through  the  weakened  face  and  through 
the  softer  metal  of  the  back. 

The  face  of  the  plate  is  crumbled,  and  a  conical  hole  made 
through  the  softer  metal,  through  which  the  projectile  passes 
practically  intact  and  in  condition  for  effective  bursting,  Fig.  183. 

The  form  of  the  cap  has  not  apparently  a  great  effect  on  the 
results.  Many  different  shapes  are  used  by  different  manufac- 
turers, some  of  which  are  shown  in  Fig.  184. 


FIG.  184. 

The  cap  increases  the  biting  angle  of  the  projectile,  the  limiting 
angle  of  impact  at  which  the  projectile  will  perforate  the  plate. 

The  following  results  have  been  obtained  in  comparative  tests 
of  capped  and  uncapped  projectiles  against  tempered  nickel  steel 
plates.  The  angle  of  impact  is  measured  from  the  normal  to  the 
plate. 


Gun. 

Thick- 
ness of 
Plate. 

Angle 
of 
Impact. 

Strik- 
ing Ve- 
locity. 

Projectile. 

Effect. 

8-inch  rifle  

Inches. 
3.5 

Degrees 
60 

1074 

Capped 

Perforated  plate 

60 

1073 

Uncapped 

Indented  plate  J  inch 

65 

1066 

Capped 

Perforated  plate 

12-inch  mortar.  .  . 

4.5 

65 

40 

40 

1077 
711 

711 

Uncapped 
Capped 

Uncapped 

Indented  plate  If  inches 
Nearly     perforated.      In- 
dentation 6  inches  deep. 
Fragment  nearly  punched 
out 
Glanced    from   plate.     In- 

dentation If  inches  deep 

It  is  stated  that  the  addition  of  the  cap  to  the  projectile  and 
the  consequent  moving  of  the  center  of  gravity  of  the  projectile 


454  ORDNANCE  AND   GUXNERY. 

toward  the  point  favorably  influences  the  trajectory,  increasing 
both  the  accuracy  and  range. 

All  projectiles  for  seacoast  guns  above  3  inches  in  caliber  will 
probably  be  provided  with  caps. 

264.  Deck  Piercing  and  Torpedo  Shell. — These  projectiles  are 
provided  for  the  12-inch  mortars.  The  torpedo  shell  is  longer 
and  of  greater  interior  capacity  than  the  deck  piercing  shell,  and 
carries  a  larger  bursting  charge  of  high  explosive.  The  bursting 
charge  for  the  deck  piercing  shell  is  64  pounds  and  for  the  torpedo 
shell  134  pounds. 

Latest  Form  of  Base  of  Shell.— A  form  of  base  with  which 
good  results  have  been  obtained  is  shown  in  Fig.  185.  The  metal 
of  the  shell  is  cut  away,  beginning  at  a  short 
distance  behind  the  band,  leaving  only  a  narrow 
ring  to  support  the  band.  In  the  perforation 
of  armor  the  band  and  the  supporting  ring  are 
sheared  off,  thus  relieving  the  projectile  of  the 
resistance  due  to  the  greater  diameter  of  the 
band. 

Shell  Tracers. — Experiments  are  now  being 
conducted  toward  the  development  of  a  pro- 
~FiG~~i85~  "  Jectile  that  will  indicate  its  line  of  flight  by  the 
emission  of  flame,  or  by  the  emission  of  some 
substance  that  will  be  visible  from  the  gun;  the  purpose  of  the 
projectile  being  to  enable  the  gun  commander  to  follow  the  flight 
of  a  projectile  from  his  gun  and  thus  determine  whether  the  gun 
is  properly  directed. 

The  tracer  for  use  at  night  consists  of  a  short  metal  cylinder 
filled  with  a  slow  burning  substance  that  emits  a  bright  flame 
during  the  flight  of  the  projectile  through  the  air.  It  may  be 
screwed  into  a  seat  prepared  in  the  base  of  any  projectile.  Igni- 
tion of  the  compound  occurs  in  the  gun. 

For  day  tracing  a  special  shell  is  prepared.  The  cavity  of  the 
shell  is  partly  filled  with  a  mixture  of  lampblack  and  water,  the 
mixture  having  the  consistency  of  thick  paint.  A  small  orifice  is 
made  through  the  base  of  the  projectile  on  one  side.  The  powder 
gases  enter  this  orifice  under  the  pressure  in  the  gun,  and  filling  the 
cavity  in  the  shell  force  from  the  orifice  during  flight  a  spray  of 


PROJECTILES. 


455 


black  liquid.    In  recent  experiments  the  flight  of  a  6-inch  day 
tracing  shell  was  followed  for  over  7200  yards. 

Hand  Grenades. — The  hand  grenade  is  a  metal  bomb  filled  with 
high  explosive  and  provided  with  one  or  more  percussion  caps  or 
fuses,  which  cause  its  explosion  on  striking  after  being  thrown. 
Hand  grenades  were  effectively  used  by  both  sides  in  the  Russo- 
Japanese  war. 

265.  Volumes  of  Ogival  Projectiles. — Assume  a  solid  cylinder, 
Fig.  186,  of  the  length  and  diameter  of  a  given  solid  shot. 

Let  d  represent  the  diameter  of  the  shot,  usu- 
ally taken  as  equal  to  the  caliber  of 
the  gun, 
L,  the  length  of  the  shot  in  calibers. 

The  volume  of  the  cylinder  is  (nd2/4)Ld. 

Let  B  represent,  in  calibers,  the  length   of  a   Ld 
cylinder  whose  diameter  is  d  and  whose  volume, 
(?rd2/4)5d,  is  equal  to  that  part  of  the  cylinder 
in  Fig.  186  that  is  outside  the  shot. 

Subtracting  this  volume  from  the  volume  of 
the  whole  cylinder  and  representing  by  78  the 
volume  of  the  solid  shot,  we  have 


.*_ 


««— --  d — • 


FIG.  186. 


y  =  -—(L—B}d=—(L-B) 

(L—B)d,  or  L— B  calibers,  is  the  length  of  a  solid  cylinder  whose 
diameter  is  the  diameter  of  the  shot  and  whose  volume  is  equal  to 
the  volume  of  the  shot.  L  —  B  is  called  the  reduced  length  of  the 
projectile  in  calibers,  as  it  is  the  length  of  a  cylinder  of  equal 
diameter  and  volume. 

B  is  a  function  of  the  radius  of  the  ogive  expressed  in  calibers. 
Its  value,  obtained  by  means  of  the  calculus,  is  given  by  the  equa- 
tion 

V4n-l      6n2-2n-l   /- 


in  which  n  is  the  radius  of  the  ogive  in  calibers.     When  n=2,  the 
'  usual  radius  of  head  in  seacoast  projectiles,  5=0.58919. 


456  ORDNANCE  AND  GUNNERY. 

For  cored  shot  the  reduced  length  is  less  than  for  solid  shot  by 
the  length  of  the  cylinder  whose  volume  is  that  of  the  interior 
cavity.  Representing  by  Bf  the  length  of  this  cylinder  in  calibers, 
the  solid  volume  of  the  cored  shot,  or  volume  of  the  metal,  is  given 
by  the  equation 


Weights  of  Projectiles.  —  Representing  the  reduced  length  by 
I,  and  dividing  the  expression  for  the  volume  of  one  projectile  by 
a  similar  expression  for  another,  we  have 


Since  the  weights  are  proportional  to  the  volumes  : 

The  weights  of  ogival  projectiles  are  proportional  to  the  prod- 
ucts of  the  cubes  of  their  diameters  by  their  reduced  lengths. 

The  weights  of  ogival  projectiles  of  the  same  caliber  are  propor- 
tionate to  their  reduced  lengths. 

As  the  standard  projectiles  for  most  of  our  guns  are  similar, 
their  dimensions  when  expressed  in  terms  of  the  caliber  are  the 
same.  The  reduced  length  is  therefore  the  same  for  all  these 
projectiles,  and  the  weights  of  the  projectiles  are  proportional  to 
the  cubes  of  the  calibers. 

266.  Thickness  of  Walls.  —  The  maximum  stress  sustained  in 
the  gun  by  the  walls  of  a  cored  projectile,  at  any  section  of  the 
projectile,  is  due  to  the  pressure  to  which  the  walls  are  subjected  in 
transmitting  to  that  part  of  the  projectile  in  front  of  the  section 
the  maximum  acceleration  attained  in  the  gun.  The  maximum 
acceleration  is  due  to  the  maximum  pressure  in  the  gun;  and  this 
pressure  being  known  the  acceleration  is  determined  by  dividing 
the  pressure  by  the  mass  of  the  projectile. 


a  being  the  acceleration,  P  the  total  maximum  pressure  on  the 
base  of  the  projectile,  and  w  the  weight  of  the  projectile.  Substi- 
tuting the  values  of  the  known  quantities  a  may  be  determined. 

a  being  known,  if  we  substitute  for  w  the  weight  of  that  part 
of  the  projectile  in  front  of  the  given  section  and  solve  the  equa- 


PROJECTILES.  457 

tion  for  P,  the  value  obtained,  which  we  will  call  Plt  will  be  the 
pressure  sustained  by  the  walls  of  the  section.  The  area  of  the 
section  is  7r(#2-r2).  The  pressure  per  unit  of  area  is  therefore  Pl 
divided  by  ~(R2-r2). 

This  pressure  must  not  exceed  the  elastic  limit  of  the  metal  for 
compression,  divided  by  a  suitable  factor  of  safety;  nor  must  it 
cause  excessive  flexure  in  the  walls.  If  it  does  the  walls  must  be 
made  thicker. 

Thickening  the  walls  will  increase  the  weight  in  front  of  the 
section  and  therefore  a  new  value  of  w  must  be  obtained  for  a 
second  determination. 

In  shrapnel  it  is  desirable  to  make  the  walls  as  thin  as  possible 
in  order  to  increase  the  number  of  bullets  that  may  be  carried. 
The  longitudinal  pressure  of  the  contained  bullets  is  borne  by  the 
thicker  base  of  the  projectile,  and  the  walls  sustain  only  the  pres- 
sure due  to  the  centrifugal  force  and  that  proceeding  from  the 
weight  of  the  head  and  fuse.  Their  thickness  will  therefore  be 
determined  by  the  requirement  that  they  must  resist  rupture  by 
the  pressure  exerted  by  the  gases  from  the  bursting  charge  when 
the  head  of  the  projectile  is  blown  off.  The  pressure  required  to 
blow  off  the  head  is  equal  to  the  resistance  offered  to  shearing  by 
the  screw  threads  and  shear  pins  of  the  head. 

A  much  greater  thickness  of  wall  than  is  needed  in  the  gun  is 
required  to  enable  a  projectile  to  withstand  the  shock  of  impact  on 
the  face  of  an  armor  plate.  The  retardation  in  this  case  is  much 
greater  than  the  acceleration  in  the  gun  and  consequently  the 
stresses  on  the  walls  are  correspondingly  greater.  As  there  is  no 
means  of  determining  the  retardation  at  impact,  the  proper  thick- 
ness of  walls  of  armor  piercing  projectiles  cannot  be  calculated, 
but  must  be  determined  by  experiment. 

We  may,  however,  by  assuming  that  the  plate  offers  a  constant 
resistance  to  the  penetration  of  the  projectile,  determine  the  thick- 
ness of  wall  necessary  in  the  projectile  to  enable  it  to  pass  through 
the  plate  and  have  any  required  velocity  on  emerging. 

Thus,  to  determine  the  thickness  of  wall  of  an  armor  piercing 
shell  that  is  required,  with  a  striking  velocity  r,  to  perforate  an 
armor  plate  of  given  thickness  and  to  have  on  emerging  a  re- 
maining velocity  v\. 


458  ORDNANCE  AND  GUNNERY. 

Let  S  be  the  constant  resistance  offered  by  the  plate 
I  the  thickness  of  the  plate,  in  feet, 
a  the  constant  retardation  of  the  projectile  during  pene- 

tration. 

The  work  performed  by  the  resistance  over  the  path  I  is  equal  to 
the  energy  abstracted  from  the  projectile  while  traversing  this 
path.  Therefore 


The  retardation  due  to  the  resistance  is  equal  to  the  resistance 
divided  by  the  mass.  Therefore 

S     v2-v12 
~M~     21 

The  pressure  sustained  by  any  section  of  the  projectile  during 
penetration  is  equal  to  the  mass  of  that  portion  of  the  projectile 
behind  the  section  multiplied  by  the  retardation.  Denoting  by  w' 
the  weight  of  that  part  of  the  projectile  behind  any  given  section, 
we  have  for  the  pressure  sustained  per  unit  of  area  at  the  section 


wf        a  w'(v 


'2— 


g  x(R2-r2}     2lg7r(R2-r2} 

R  and  r  must  be  given  such  values,  that  is,  the  thickness  of  the 
walls  must  be  such  that  p  will  not  exceed  the  elastic  limit  of  the 
metal  for  compression,  or  that  the  flexure  of  the  walls,  considering 
the  shell  as  a  hollow  column,  will  not  be  sufficient  to  cause  rupture. 

267.  Sectional  Density  of  Projectiles. — It  has  been  found  by 
experiment,  as  explained  in  exterior  ballistics,  that  the  retardation 
in  the  velocity  of  a  fired  projectile,  due  to  the  resistance  of  the  air, 
is  expressed  by  an  equation  that,  for  any  fixed  atmospheric  condi- 
tions and  standard  form  of  projectile,  may  be  put  in  the  form 

_     d? 

w' 

R  representing  the  retardation,  A  a  constant,  d  the  diameter  of  the 
projectile,  w  its  weight,  and  f(v)  some  function  of  its  velocity. 


PROJECTILES.  459 

For  a  given  velocity  it  is  apparent  that  the  retardation  will  in- 
crease directly  with  the  square  of  the  diameter  of  the  projectile  and 
inversely  with  its  weight;  or,  more  concisely,  the  retardation  will 
increase  directly  with  the  fraction  cP/w. 

The  reciprocal  of  this  fraction,  or  w/d2.  will  therefore  be  the 
measure  of  the  capacity  of  the  projectile  to  resist  retardation,  that 
is,  to  overcome  the  resistance  of  the  air. 

The  fraction  w/d2  is  called  the  sectional  density  of  the  projectile. 
w/\nd2  is  the  weight  of  the  projectile  per  unit  area  of  cross  section, 
and  w/d2  is  taken  as  the  measure  of  this  weight,  -/4  being  con- 
stant. 

The  sectional  density  is  of  importance  in  considering  the  mo- 
tion of  the  projectile  both  in  the  air  and  hi  the  gun. 

EFFECT  ON  THE  TRAJECTORY. — The  greater  the  sectional  den- 
sity of  the  projectile,  the  less  the  value  of  its  reciprocal,  the  factor 
d?/w  in  the  above  equation,  and  consequently  the  less  is  the  value 
of  the  retardation  of  the  projectile. 

Of  two  projectiles  fired  with  the  same  initial  velocity  and  eleva- 
tion, the  projectile  with  the  greater  sectional  density  will  therefore 
lose  its  velocity  more  slowly  and  will  attain  a  greater  range.  For 
any  given  range  it  will  be  subjected  for  a  less  time  to  the  action  of 
gravity  and  other  deviating  causes,  and  will  therefore  have  a 
flatter  trajectory  and  greater  accuracy. 

The  advantages  of  increased  sectional  density  are  therefore 
increased  range,  greater  accuracy,  and  a  flatter  trajectory. 

The  sectional  density  may  be  increased  by  increasing  the 
weight  of  the  projectile  or  by  decreasing  its  diameter.  The 
weight  of  a  projectile  for  any  gun  may  be  increased  by  increasing 
its  length.  This  has  been  done  with  modern  projectiles  for  large 
guns  until  the  length  is  from  3J  to  4  calibers.  In  small  arms  the 
weight  is  increased  by  the  use  of  lead  in  the  bullet.  Increase  in 
sectional  density  by  decrease  in  diameter  is  found  in  the  modern 
small  arms  of  reduced  caliber,  the  weight  and  diameter  of  the 
projectile  having  been  reduced  in  such  proportions  as  to  increase 
its  sectional  density. 

EFFECT  ON  THE  Gux. — An  increase  in  the  weight  of  the  pro- 
jectile requires  an  increased  pressure  in  the  bore  of  the  gun  if  the 
initial  velocity  is  to  be  maintained.  The  maximum  pressure  for 


460  ORDNANCE  AND  GUNNERY. 

any  gun  being  fixed,  it  has  been  possible  to  increase  the  weight  and 
sectional  density  of  projectiles  only  by  the  use  of  improved  pow- 
ders, which  while  they  exert  no  greater  maximum  pressures  exert 
higher  pressures  along  the  bore  of  the  gun.  The  mean  pressure  on 
the  projectile  is  therefore  greatly  increased,  and  to  withstand  the 
increased  pressure  the  chase  of  the  gun  is  made  stronger. 

MANUFACTURE   OF   PROJECTILES. 

268.  Cast  Projectiles. — A  wooden  pattern  of  the  shape  of  the 
projectile  is  first  made,  the  dimensions  of  the  pattern  being  slightly 
greater  than  the  dimensions  desired  in  the  projectile,  in  order  to 
allow  for  contraction  of  the  metal  in  cooling.  The  pattern  is  in 
one  or  more  parts,  depending  upon  its  size.  The  pattern  shown  in 
Fig.  187  is  in  two  parts  separated  at  the  line  6.  The  parts  are 
slightly  coned  from  this  line  to  facilitate  withdrawal  from  the 
mold.  For  hollow  projectiles  a  core  box  is  also  made  similar  in 
its  interior  dimensions  to  the  cavity  in  the  shell.  The  core,  e  Fig. 
187,  made  of  core  sand  mixed  with  adhesives,  is  formed  in  the 
core  box  around  a  hollow  metal  spindle  wound  with  tow.  The 
heat  of  the  casting  burns  the  tow,  and  the  gases  from  the  core 
pass  out  through  the  hollow  spindle. 

Fig.  188  shows  a  mold  prepared  for  casting  a  shell.  The  outer 
box,  called  the  flask,  is  in  two  sections  parting  at  the  line  xy.  In 
the  lower  part  the  sand  is  molded  around  the  pattern,  which  is 
also  divided  into  two  parts  on  the  same  line.  In  the  upper  part 
of  the  flask  the  remainder  of  the  mold  is  made  and  the  core  at- 
tached in  its  proper  position  by  means  of  the  frame  a  bolted  to 
the  flask.  The  gate  6  and  the  riser  c  are  also  formed  in  the  mold, 
the  riser  being  considerably  greater  in  diameter  than  shown  in  the 
figure.  The  patterns  are  withdrawn  and  the  parts  of  the  mold 
brought  together  and  bolted. 

The  molten  metal  enters  through  the  gate  6,  generally  in  a 
tangential  direction,  so  that  the  metal  in  the  mold  has  a  circular 
motion  which  assists  in  the  escape  of  the  gases  and  brings  the 
impurities  to  the  center  and  top.  The  mold  is  filled  with  the 
metal  to  the  top  of  the  riser,  where  the  impurities  collect.  The 
pressure  of  the  liquid  metal  in  the  riser  assists  in  making  the  cast- 


PROJECTILES. 


461 


ing  sound,  and  affords  a  means  of  adding  molten  metal  as  the 
casting  shrinks  in  cooling. 

Solid  shot  are  cast  head  down  in  order  that  the  dense  metal 
may  be  in  the  head  of  the  shot.  Shells  are  cast  base  down,  that  the 
base  of  the  shell  may  be  sound  and  free  from  cavities  that  would 
allow  the  powder  gases  to  pass  into  the  interior  and  ignite  the 
bursting  charge. 


A 


--6 


m 


FIG.  187. 


FIG.  188. 


Chilled  Projectiles. — For  use  against  wrought  iron  armor  the 
heads  of  cast  projectiles  were  hardened  in  casting  by  the  process 
of  chilling.  A  comparatively  thin  iron  mold  the  shape  of  the 
head  and  in  contact  with  it  was  fixed  in  the  sand  around  the  head 
of  the  projectile.  This  served  to  rapidly  conduct  the  heat  away 
from  the  head  of  the  projectile,  causing  it  to  cool  rapidly  and 
givirig  it  great  hardness.  These  projectiles  are  no  longer  used. 

Forged  Projectiles. — The  steel  for  a  forged  projectile  is  cut 
from  a  cast  ingot,  and  is  then  bored,  forged,  and  turned  to  finished 
dimensions.  Armor  piercing  projectiles  are  in  addition  treated 


462 


ORDNANCE  AND  GUNNERY. 


with  some  secret  process  of  tempering  to  give  them  the  hardness 
and  toughness  necessary  for  the  perforation  of  armor. 

269.  Requirements  in  Manufacture. — The  qualities  of  the 
metal  of  the  projectile  are  prescribed  as  follows:  For  cast  iron, 
tensile  strength  27,000  Ibs.  per  square  inch;  for  steel,  in  what  are 
called  common  shell,  that  is,  those  of  the  smaller  calibers,  tensile 
strength  85,000  Ibs.  For  armor  piercing  projectiles  the  tensile 
strength  or  elastic  limit  is  not  specified,  further  than  by  the  re- 
quirement that  the  projectiles  in  a  lot  shall  not  vary  in  tensile 
strength  by  more  than  20,000  Ibs.  The  strength  of  these  shells  is 
determined  by  actual  firing  against  armor.  The  cap  must  be  of 
steel  whose  tensile  strength  does  not  exceed  60,000  Ibs.,  with  an 
elongation  at  rupture  of  30  per  cent,  and  a  reduction  in  area  of 
45  per  cent. 

The  base  plugs  of  all  projectiles  are  made  of  forged  steel. 

Inspection  of  Projectiles. — The  dimensions  of  the  projectiles 
are  tested  by  means  of  calipers,  and  profile  and  ring  gauges.  The 
slight  variations,  called  tolerances,  allowed  from  the  standard 
dimensions  are  specified  for  each  dimension,  and  the  gauges  for 
any  projectile  are  constructed  for  the  maximum  and  minimum 
of  the  particular  dimension.  Thus  for  the  diameter  of  the  band 
there  are  two  ring  gauges,  one  a  maximum,  the  other  a  minimum, 
and  similarly  for  other  diameters.  Maximum  and  minimum  plug 
gauges  are  applied  to  the  threads  of  the  fuse  hole.  A  ring  gauge 
is  shown  in  Fig.  189.  A  profile  gauge  or  templet  is  shown  at  a  in 
Fig.  190. 


a 


FIG.  189. 


FIG.  190. 


Eccentricity  in  the  cavity  of  the  projectile  is  determined  by 
rolling  the  projectile  along  two  rails,  a  Fig.  191,  placed  on  a  flat 
surface.  Irregular  movement  of  the  projectile  denotes  eccen- 
tricity, which  may  be  measured  by  means  of  the  calipers,  d,  shown 
in  the  figure. 


PROJECTILES. 


463 


For  the  detection  of  holes  or  cracks  through  the  walls  of  hollow 
projectiles  all  such  projectiles  are  subjected  to  an  interior  hy- 
draulic pressure.  A  pressure  of  500  Ibs.  per  sq.  in.  is  applied  for 
one  minute  to  steel  projectiles,  and  a  pressure  of  300  Ibs.  for  two 
minutes  to  those  of  cast  iron. 

To  determine  whether  the  treatment  received  by  the  armor 
piercing  shot  in  the  tempering  process  has  left  in  the  shot  initial 
strains  that  might  cause  rupture  in  store  or  in  firing,  these  shot  are 
cooled  to  a  temperature  of  40  degrees  F.  and  then  suddenly  heated 


Er 


FIG.  191. 


by  being  plunged  into  boiling  water.  When  thoroughly  heated  by 
the  water,  the  projectile  is  suddenly  cooled  by  being  half  inserted, 
with  its  axis  horizontal,  in  a  bath  of  water  at  40  degrees  F.  After 
a  brief  interval  it  is  turned  180  degrees  for  a  like  immersion  of  the 
other  half.  Three  days  must  elapse  after  the  tempering  of  the 
projectile  before  this  test  is  applied.  The  necessity  of  the  test  is 
indicated  by  the  not  infrequent  bursting  of  the  projectiles  in  the 
shops  after  tempering.  This  test  is  not  applied  to  armor  piercing 
shell.  The  thinner  walls  of  these  projectiles  are  more  uniformly 
affected  by  the  tempering  process. 


464  ORDXANCE  AND  GUNXERY. 

The  interior  walls  of  hollow  projectiles  are  coated  with  a  lacquer 
of  turpentine  and  asphalt  for  the  purpose  of  making  them  smooth 
and  of  reducing  the  friction  between  the  walls  and  the  bursting 
charge. 

Ballistic  Tests. — Each  class  of  projectile  is  subjected  to  a 
allistic  test  under  conditions  assimilating  the  conditions  of  ser- 
vice. For  the  purpose  of  the  test  two  or  more  projectiles  are 
selected  from  each  lot  pre -rented.  The  projectiles  tested  are  filled 
with  sand  in  place  of  a  bursting  charge,  and  after  the  test  must  be 
hi  condition  for  effective  bursting. 

Armor  piercing  shot  are  fired  against  hard  faced  Krupp  armor 
plate,  from  1  to  1$  calibers  thick,  secured  to  timber  backing.  The 
striking  velocities  of  the  shot  from  8,  10,  and  12  inch  rifles 
against  plates  one  caliber  thick  are  near  to  1750  feet,  which  corre- 
sponds to  ranges  of  about  3000,  4000,  and  5000  yards,  respectively 
from  the  three  guns.  The  shot  is  required  to  perforate  the  plate 
unbroken  and  then  be  in  condition  for  effective  bursting. 

Armor  piercing  shells  must  meet  similar  conditions,  the  thick- 
ness of  the  plate  being  one  half  the  caliber  of  the  shell,  and  the 
striking  velocities,  1420  f.  s.  for  5-inch  shell,  1220  f.  s.  for  6-inch 
shell,  and  920  f.  s.  for  8-,  10-,  and  12-inch  shell. 

12-inch  deck  piercing  shell  must  perforate  a  4|-inch  nickel 
steel  protective  deck  plate  at  an  angle  of  impact  of  60  degrees. 

12-inch  torpedo  shell  are  fired  into  a  sand  butt  from  a  gun  in 
which  the  chamber  pressure  must  be  37,000  Ibs. 

Common  steel  shell  for  seacoast  guns  of  small  caliber  are 
tested  with  service  velocities  against  tempered  steel  plates  from  3 
to  5  inches  thick,  depending  on  the  caliber  and  service  velocity  of 
the  projectile. 

The  shell  for  field  and  mountain  guns  are  fired  into  sand,  with 
a  pressure  in  the  gun  12  per  cent  greater  than  the  service  pressure 
and  with  at  least  the  service  velocity. 

Tests  are  also  made  to  determine  whether  the  fragmentation  of 
the  projectile  on  bursting  is  satisfactory. 

The  Painting  of  Projectiles. — Projectiles  aro  so  painted  as  to 
indicate  the  metal  of  which  they  are  formed  and  the  character  of 
the  bursting  charge.  The  greater  part  of  the  body  is  black.  A 
broad  colored  band  around  the  projectile  over  the  center  of  gravity 


PROJECTILES.  465 

indicates  by  the  color  whether  the  projectile  is  of  iron,  cast  or 
chilled,  or  of  steel,  cast  or  forged. 

The  color  of  the  base  indicates  whether  the  projectile  is  charged 
with  powder  or  with  high  explosive.  In  assembled  ammunition 
the  base  color  is  painted  in  a  band  just  above  the  band  of  the 
projectile. 


CHAPTER  XI. 
ARMOR. 

270.  History. — The  use  of  armor  for  the  protection  of  ships  of 
war  began  in  France  in  1855  and  soon  became  general.  The  first 
armor  was  of  wrought  iron.  This  metal  opposed  a  sufficient  re- 
sistance to  the  round  cast  iron  projectiles  of  that  time  and  to  the 
elongated  cast  iron  shot  of  a  later  date.  As  the  power  of  guns 
increased  and  chilled  projectiles  came  into  use  wrought  iron  armor 
became  ineffective.  It  was  replaced  about  1880  by  compound 
armor,  which  consisted  of  a  wrought  iron  back  and  a  hard  steel 
face.  Compound  armor  was  made  either  by  running  molten  steel 
on  the  previously  prepared  wrought  iron  back  or  by  welding  a 
plate  of  steel  to  another  of  wrought  iron  by  running  molten  steel 
between  them,  both  plates  being  previously  brought  to  a  welding 
heat.  The  hard  steel  face  opposed  a  great  resistance  to  penetra- 
tion of  the  shot  and  caused  the  shot  to  expend  its  energy  in  shatter- 
ing itself.  At  the  same  time  it  distributed  the  stress  over  an  in- 
creased section  of  the  iron  back,  and  the  toughness  of  the  wrought 
iron  served  to  hold  the  plate  together.  The  chief  defect  of  the 
compound  plate  was  due  to  the  difficulty  of  obtaining  intimate 
union  between  the  two  metals,  and  lay  in  the  tendency  of  the  steel 
face  to  flake  off  over  considerable  areas.  The  basic  principle  of 
this  armor,  the  hard  face  and  the  tough  back,  is  still  maintained 
in  the  construction  of  the  most  modern  armor. 


NOTE. — This  chapter  is  largely  derived  from  the  chapter  on  armor  by 
Lieutenant  Commander  Cleland  Davis,  U.  S.  Navy,  in  Fullam  and  Hart's 
Text  Book  of  Ordnance  and  Gunnery,  1905. 

466 


ARMOR.  467 

At  the  same  time  that  the  compound  plate  was  used  by  Great 
Britain  and  other  powers  the  all  steel  plate  was  being  used  by 
France,  the  effectiveness  of  the  two  plates  being  about  equal. 

In  1889  the  homogeneous  nickel-steel  plate,  markedly  superior 
to  the  steel  plate  in  toughness  and  resisting  power,  was  introduced. 
The  Harvey  treatment  of  the  nickel-steel  plate,  developed  in  the 
United  States  in  1890,  still  further  increased  the  resisting  power 
of  armor,  and  in  1895  the  Krupp  process  followed  with  further 
improvement. 

Harvey  and  Krupp  Armor. — The  principle  employed  in  the 
manufacture  of  armor  by  these  two  processes  is  the  same.  In 
both,  the  face  of  the  plate  is  made  extremely  hard  by  supercarbon- 
ization  and  subsequent  chilling.  The  superiority  of  the  Krupp 
plate  appears  to  be  due  to  the  composition  of  the  steel.  The 
Harvey  plate  is  made  of  a  manganese  nickel  steel,  while  in  the 
Krupp  plate  chromium  is  also  present,  and  in  greater  quantity 
than  the  manganese.  The  composition  of  the  two  plates,  in  per- 
centages, is  given  as  follows: 

C.  Mn.  Si.  P.  S.  Ni.  Cr. 

Harvey 0.30       0.80       0.10       0.04       0.02       3.25       0.00 

Krupp 0.35       0.30       0.10       0.04       0.02       3.50       1.90 

The  nickel,  and  to  a  certain  extent  the  manganese,  give  great 
strength  and  toughness  to  the  metal,  while  the  chromium  makes 
the  metal  more  susceptible  to  the  treatment  that  gives  the  desired 
qualities  to  the  finished  plate.  First,  it  permits  the  attainment  of 
a  very  tough  fibrous  condition  throughout  the  body  of  the  plate 
that  makes  it  less  liable  to  crack;  second,  it  gives  the  metal  an 
affinity  for  carbon  which  enables  supercarbonization  to  a  greater 
depth;  third,  it  increases  the  susceptibility  of  the  metal  to  tem- 
pering, which  gives  a  greater  depth  of  chill.  These  are  the  quali- 
ties that  mark  the  superiority  of  Krupp  armor. 

Even  when  carbonization  of  the  plates  is  effected  in  the  same 
manner,  carbon  will  be  absorbed  to  a  greater  depth  in  the  Krupp 
than  in  the  Harvey  armor,  giving  a  greater  depth  of  hardened  face 
and  an  increased  resistance  to  penetration  of  about  20  per  cent. 

271.  Manufacture  of  Armor. — The  steel,  of  proper  composi- 
tion, is  made  in  the  open  hearth  furnace  and  cast  into  an  ingot  of 
the  shape  shown  in  Fig.  192.  The  head  of  the  ingot  affords  a 


468 


ORDNANCE  AND  GUNNERY. 


means  for  the  attachment  of  the  chains  of  the  cranes  employed  in 
handling  it.  A  long  heavy  beam  is  used  to  counterbalance  the 
weight  of  the  plate  when  slung  in  the  chains. 

When  stripped  from  the  mold  and  cleaned,  the  ingot  is  heated 
in  a  furnace  and  then  forged,  as  shown  in  Fig.  193,  under  an 
immense  hydraulic  press  capable  of  exerting  a  total  pressure  of 
about  15,000  tons.  The  forging  reduces  the  thickness  of  the  plate 


144" 


FIG.  192. 

and  increases  its  length  and  breadth.    The  plate  is  then  rough 
machined  approximately  to  finished  dimensions. 

CARBONIZING. — The  carbonization  of  the  face  of  the  plate  is 
effected  by  one  of  two  methods:  the  cementation  process,  or  the 
gas  carbonizing  process.  The  cementation  process  consists  in 
covering  the  surface  of  the  plate  with  carbonaceous  material, 
usually  a  mixture  of  wood  and  animal  charcoal,  heating  the  plate 
to  a  temperature  of  about  1950  degrees,  and  maintaining  it  at 
this  temperature  for  a  sufficient  time  to  accomplish  the  required 


ARMOR.  469 

degree  of  carbonization.  A  covering  of  sand  protects  the  face  of 
the  plate  and  the  carbonizing  material  from  the  flames  of  the 
furnace,  and  excludes  the  air.  From  four  to^ten  days,  depending 
on  the  thickness  of  the  plate,  are  required  to  bring  the  plate  to  the 
desired  temperature,  and  a  further  period  of  from  four  to  ten  days 
to  effect  the  carbonization  of  the  face.  Under  the  action  of  the 
heat  the  carbon  is  absorbed  into  the  face  of  the  plate,  and  pene- 
trates into  the  interior,  the  quantity  of  the  absorbed  carbon  dimin- 
ishing from  the  surface  inward. 

The  gas  carbonizing  process  consists  in  passing  coal  gas  along 
the  face  of  the  plate  heated  in  a  furnace  to  about  2000  degrees. 
The  heat  decomposes  the  gas,  which  deposits  carbon  on  the  face 
of  the  plate,  and  the  carbon  is  absorbed  as  in  the  cementation 
process. 

REFORGING  AND  BENDING. — After  being  cleaned  of  the  scale 
that  is  formed  on  it  in  the  process  of  carbonization  the  plate  is  re- 
forged  to  its  final  thickness.  It  is  then  annealed  and  bent  to  the 
desired  shape  in  a  hydraulic  press.  The  operation  of  bending  an 
armor  plate  in  a  9000  ton  press  is  shown  in  Fig.  194. 

HARDENING. — For  tempering,  the  plate  is  uniformly  heated  to 
a  high  temperature  and  quickly  cooled  or  chilled  by  cold  water 
sprayed  upon  it  under  a  pressure  of  about  23  pounds  to  the  square 
inch. 

In  Krupp  plates  as  first  made  the  tempering  produced  cracks 
over  the  whole  hard  surface  of  the  plate,  some  of  them  a  quarter 
of  an  inch  wide  and  extending  some  distance  into  the  plate.  The 
cracks  were  characteristic  of  the  plate  and  were  not  considered 
abnormal,  the  resistance  of  the  plate  even  with  the  cracks  being 
greater  than  that  of  plates  made  by  other  processes.  With  im- 
provement in  the  process  of  manufacture  smoother  plates  were 
produced,  and  in  many  of  the  latest  plates  the  surface  appears 
continuous  to  the  naked  eye.  When  etched  with  acid,  however, 
the  face  is  found  to  be  covered  with  a  network  of  fine  lines  and 
presents  an  appearance  similar  to  that  of  crackled  glass. 

272.  Armor  Bolts. — The  armor  plates  are  fastened  to  the  sides 
of  ships  by  means  of  nickel-steel  bolts.  These  are  of  such  strength 
that  they  are  not  broken  by  the  impact  of  projectiles  that  badly 
crack  the  plate.  The  bolts  pass  through  the  sides  of  the  ship  and 


470 


ORDNANCE  AND  GUNNERY. 


are  screwed  into  the  soft  back  of  the  armor  plate.  To  insure  a 
good  fit  of  the  plate,  and  at  the  same  time  to  lengthen  the  armor 
bolt  so  that  its  deformation  per  unit  of  length  under  the  stresses 
of  impact  may  not  be  excessive,  wood  backing  is  used  between 
the  armor  plate  and  the  ship's  side.  The  wood  backing  is  being 
reduced  in  thickness  and  the  tendency  is  to  discard  it  altogether. 
Figs.  195  and  196  show  types  of  bolts  for  armor  with  and  without 
wood  backing. 


FIG.  195. 

The  threads  on  the  bolts  are  all  plus  threads,  so  that  the  bolt  is 
of  uniform  strength.     A  calking  of  marline  or  oakum  surrounds 

the  bolt  to  prevent  leakage  through  the 
bolt  hole.  A  steel  washer  is  under  the 
head  of  the  bolt.  A  rubber  washer  has 
also  been  used  under  the  steel  washer 
to  diminish  the  suddenness  of  any 
strain  on  the  bolt  head. 

Armor  bolts  vary  in  diameter  from 
1.5  inches  for  plates  5  inches  thick  or 
less  to  2.4  inches  for  plates  9  inches 
FlG   196  thick  and  upward. 

In  number  they  are  provided  one 

for  every  five  square  feet  of  surface  as  far  as  the  framing  of  the 
ship  will  permit. 


ARMOR.  471 

Ballistic  Test  of  Armor. — The  U.  S.  Xavy  specifications  re- 
quire as  a  test,  before  acceptance  of  Krupp  and  Harvey  armor, 

three  impacts  of  capped  shells  against   a  specimen  plate,  with 
velocities  as  given  hi  the  following  table. 

Caliber  Capped                               Plate  Striking 

of  Gun,  Projectile,                        Thickness,  Velocity, 

Inches.  Pounds.                            Inches.  f.  s. 

6  105               5  1416 

6  105            6  1608 

6  105  7  1791 

7  165  6  1416 
7  165            7  1578 

7  165  8  1732 

8  260  7  1412 
8  260            8  1552 
8  260            9  1685 

10  510            9  1458 

10  510            10  1569 

10  510            11  1676 

12  870            11  1412 

12  870            12  1501 


The  first  impact  in  the  center  of  the  plate  must  not  develop 
a  through  crack  to  an  edge  of  the  plate,  and  no  part  of  the  pro- 
jectile shall  get  entirely  through  the  plate  and  backing.  On  the 
second  and  third  impacts  no  part  of  the  projectile  shall  get  en- 
tirely through  the  plate  and  backing.  The  impacts  shall  not  be 
nearer  than  3J  calibers  to  each  other  or  to  an  edge  of  the  plate. 

Comparing  the  requirements  for  plates  attacked  by  the  8,  10, 
and  12  inch  guns  with  the  requirements  of  the  ballistic  tests  of 
armor  piercing  projectiles  for  the  land  service,  page  464,  it  will  be 
seen  that  the  armor  plates  one  caliber  thick  are  tested  with 
velocities  about  200  feet  less  than  those  at  which  the  projectiles 
from  land  guns  are  required  to  perforate  similar  plates. 

Characteristic  Perforations. — Characteristic  perforations  in 
hardened  and  unhardened  armor  are  shown  in  Figs.  197  and  198, 
the  front  face  of  the  plate  being  uppermost  hi  each  figure.  The 
face  of  the  hardened  armor,  Fig.  197,  breaks  and  crumbles  under 
impact,  while  the  metal  of  the  unhardened  plate,  Fig.  198,  being 
softer  and  more  tenacious,  flows  under  the  pressure  of  the  projec- 
tile in  the  direction  of  least  resistance  and  forms  a  combing  hi 


472 


ORDXAXCE   AXD  GUNNERY. 


front  of  the  plate.  When  the  projectile  reaches  the  back  of  the 
hardened  armor  the  metal  of  the  back,  being  prevented  from 
flowing  by  the  hard  face,  breaks  out  in  one  or  more  pieces,  leaving 


FIG.  197. 


a  broad  based  conical  hole  through  the  back  and  producing  but 
slight  bulging  of  the  rear  surface  of  the  plate. 

As  the  metal  of  the  unhardened  plate  is  of  the  same  constitu- 
tion throughout,   the  perforation  does  not  exhibit  the  marked 


FIG.  198. 

differences  shown  in  the  hardened  plate.  The  metal  of  the  back 
part  of  the  plate  flows  to  the  rear,  producing  a  greater  bulging  of 
the  rear  surface. 

273.  Armor  Protection  of  Ships. — The  armor  carried  by  ships 
of  war  is  of  various  thicknesses,  depending  upon  the  size  and  pur- 
pose of  the  ship  and  on  the  position  of  the  armor  on  or  in  the  ship. 
The  thickest  armor  is  used  to  protect  the  water  line  and  the  vital 
parts  of  battleships.  The  present  practice  in  the  United  States  is 
to  protect  the  whole  length  of  the  water  line  with  a  belt  of  armor 
8  feet  wide  extending  4£  feet  above  the  water  line  and  3J  feet 
below  it. 


ARMOR.  473 

This  belt,  see  Fig.  199,  has  its  maximum  thickness  over  that 
part  of  the  ship  that  contains  the  machinery  and  the  magazines. 
The  thickness  diminishes  from  the  mid-ship  section  and  is  least  at 
the  bow  and  stern. 

The  gun  turrets  are  protected  in  front  by  the  thickest  armor. 
Armor  of  less  thickness  covers  the  casemates,  barbettes,  and  sides 
of  the  turrets,  the  thickness  depending  upon  the  importance  of 
the  part  protected  and  upon  its  exposure  to  hostile  fire.t1. 

An  armored  deck  of  a  thickness  to  prevent  penetration  by  the 
fragments  of  exploded  shell  extends  the  whole  length  of  the  ship. 
This  deck,  the  berth  deck,  Figs.  199  and  200,  is  flat  over  the 
machinery  and  boiler  spaces  and  slopes  downward  at  the  sides 
and  at  the  bow  and  stern  to  the  bottom  of  the  belt  armor.  On 
the  heaviest  ships  the  armored  deck  has  a  thickness  of  two  inches 
over  the  flat  part  and  four  inches  on  the  slopes,  the  thickness 
being  reduced  over  the  flat  part  in  order  to  reduce  the  weight. 
The  gun  deck,  next  above  the  armored  deck,  is  sometimes  an 
armored  splinter  deck  one  inch  thick. 

Across  the  main  body  of  the  ship,  bow  and  stern,  extends 
heavy  athwartship  armor,  which,  with  the  armored  barbettes  and 
turrets,  provides  protection  to  the  body  of  the  ship  from  fire  from 
the  front  or  rear.  Thus  with  the  side  armor  the  main  body  of 
the  ship  becomes  an  armored  box,  within  which  the  crew,  the 
machinery,  the  magazines,  and  the  guns  are  protected. 

With  the  improvements  that  have  taken  place  in  armor  within 
the  last  fifteen  years  there  has  been  a  gradual  reduction  in  the 
thickness  of  armor  carried  by  ships  of  the  various  classes. 

The  battleship  Oregon,  built  in  1893,  has  a  water  line  belt  18 
inches  in  thickness,  while  the  battleship  Connecticut,  commis- 
sioned in  September,  1906,  has  but  11  inches  of  armor  at  her  water 
line. 

The  arrangement  of  the  armor  on  the  battleship  Connecticut 
is  shown  in  Figs.  199  and  200. 

Definitions. — The  following  definitions  will  assist  toward  a 
ready  understanding  of  the  figures. 

TURRET. — A  revolving  armored  structure  in  which  one  or  two 
guns  are  mounted.  The  guns  revolve  with  the  turret  and  are 
completely  enclosed  with  the  exception  of  the  chase  of  the  gun, 


474 


ORDNANCE  AND  GUNNERY. 


ARMOR. 


475 


which  projects  through  a  port  hole  in   the  front    plate   of   the 
turret. 

BARBETTE. — A  fixed  circular  structure,  armored,  which  pro- 
tects the  mechanism  for  the 
ammunition  supply  of  the  gun 
mounted  above  it  and  the 
mechanism  of  the  turret  con- 
taining the  gun. 

CASEMATE. — An  isolated  gun 
position  for  a  broadside  gun 
with  fixed  armor  protection. 
The  casemate  completely  en- 
closes the  gun  with  the  excep- 
tion of  the  chase,  which  projects 
through  a  port  hole. 

CENTRAL  CITADEL. — Armor 
enclosing  a  series  of  broadside 
guns.  There  may  or  may  not 
be  splinter  bulkheads  between 
the  guns.  With  the  bulkheads 

completely  enclosing  the  guns  the  citadel  becomes   a  series  of 
casemates. 

274.  Chilled  Cast  Iron  Armor. — This  armor  on  account  of  its 
thickness  and  great  weight  is  used  only  on  land.  It  is  manu- 
factured by  Gruson  of  Germany.  It  is  cast  in  large  blocks  whose 
outer  faces  are  made  very  hard  by  chilling.  The  blocks  are  then 
built  into  turrets,  usually  of  rounded  shape. 

On  account  of  the  great  weight  and  hardness  of  the  metal  and 
the  rounded  shape  of  the  turrets,  this  armor  affords  better  pro- 
tection than  any  other  armor. 

Gun  Shields. — Guns  of  6  inches  caliber  and  less  mounted  in 
barbette  in  seacoast  fortifications  are  provided  with  shields  per- 
manently attached  to  their  carriages.  The  shields  are  made  of 
Krupp  plate  4|  inches  thick.  The  requirements  of  the  ballistic 
test  for  these  shields  are  as  follows. 

The  shield,  firmly  supported  by  a  backing  of  oak  timbers,  is 
subjected  to  three  shots  from  a  5-inch  gun.  The  striking  velocity 
of  the  shot  is  1500  feet  and  the  impact  normal.  On  the  first  im- 


FIG.  200. 


476  ORDNANCE  AND  GUXNERY. 

pact,  near  the  center  of  the  shield,  no  portion  of  the  projectile 
shall  get  through  the  shield,  nor  shall  any  through  crack  develop  to 
an  edge  of  the  shield.  The  other  two  impacts  are  so  located  that 
no  point  of  impact  shall  be  less  than  three  calibers  of  the  projectile 
from  another  point  of  impact  or  from  an  edge  of  the  shield.  At 
the  second  and  third  impacts  no  projectile  or  fragment  of  projectile 
shall  go  entirely  through  the  shield. 

The  supports  that  hold  the  shield  to  the  carriage  are  very  heavy 
ribbon-shaped  springs,  which'  reduce  the  stress  on  the  carriage  from 
the  impact  on  the  shield.  The  springs  are  of  great  strength  in 
order  to  withstand  the  shock  of  impact.  They  are  made  of  steel 
with  a  tensile  strength  of  110,000  Ibs.,  elastic  limit  75,000  Ibs., 
e  ongation  at  rupture  15  per  cent,  contraction  of  area  25  per  cent. 

The  fastening  bolts  must  have  a  tensile  strength  of  80,000  Ibs., 
and  an  elongation  at  rupture  of  27  per  cent. 

The  shields  are  curved  around  the  front  of  the  carriage  and  are 
inclined  upward  and  to  the  rear  at  an  angle  of  40  degrees.  The 
chase  of  the  gun  protrudes  through  a  hole  in  the  shield  and  other 
holes  are  provided  for  sighting  purposes. 

Fig.  201  shows  the  arrangement  of  the  shield  on  a  6-inch  bar- 
bette carriage. 

Shields  will  probably  be  provided  for  all  barbette  carriages. 

It  is  still  a  matter  of  discussion  as  to  whether  advantage  is 
derived  by  the  use  of  gun  shields,  for  while  they  serve  to  keep 
out  the  smaller  projectiles  they  also  serve  to  determine  the  burst- 
ing of  larger  projectiles  whose  destructive  power  may  be  sufficient 
to  disable  the  gun  and  wholly  destroy  the  gun  detachment.  With- 
out the  shields  these  projectiles  would  in  many  instances  pass  by, 
doing  little  or  no  harm. 

Field  Gun  Shields. — Shields  of  hardened  steel  plate  two- 
tenths  of  an  inch  thick  are  attached  to  the  gun  carriage  and  caisson 
for  the  3-inch  field  gun.  These  shields  are  tested  by  firings,  at  a 
range  of  100  yards,  with  the  30  caliber  rifle,  using  steel  jacketed 
bullets  with  2300  feet  muzzle  velocity.  The  plate  must  not  be 
perforated,  cracked,  broken,  or  materially  deformed. 

The  front  of  the  caisson  chest  is  made  of  the  same  material  as 
the  shields  and  has  the  same  thickness.  The  door  of  the  chest, 
which  opens  upward  to  an  angle  of  30  degrees,  is  made  of  hardened 
steel  plate  TVV  of  an  inch  thick. 


CHAPTER  XII. 
PRIMERS  AND  FUSES  FOR  CANNON. 

275.  Classification. — Primers  are  the  means  employed  to 
ignite  the  powder  charges  in  guns. 

They  may  be  divided,   according  to   the  method  by  which 
ignition  is  produced,  into  three  classes: 
Friction  primers, 
Electric  primers, 
Percussion  primers. 

Combination  primers  are  those  so  constructed  that  they  may 
be  fired  by  any  two  of  the  above  methods.  Primers  that  close 
the  vent  against  the  escape  of  the  powder  gases  are  called  ob- 
turating  primers. 

All  primers  should  be  simple  in  construction,  safe  in  handling, 
certain  in  action  and  not  liable  to  deterioration  in  store.  Electric 
primers  in  addition  should  be  uniform  as  to  the  electric  current 
required  for  firing. 

Common  Friction  Primer. — The  primer  known  as  the  common 
friction  primer,  formerly  used  in  all  cannon,  is  shown  in  Fig.  202. 

The  body  b  and  the  branch  d  are  copper  tubes.  The  tube  b  is 
filled  with  rifle  powder,  and  is  closed  at  its  lower  end  by  a  wax 
stopper  a.  The  tube  d  is  filled  with  the  friction  composition, 
whose  ingredients  are  chlorate  of  potash,  sulphide  of  antimony, 
ground  glass,  and  sulphur  mixed  with  a  solution  of  gum  arabic. 
Imbedded  in  the  friction  composition  is  the  serrated  end  of  the 
copper  wire  c,  the  other  end  of  the  wire  being  formed  into  a  loop 
for  attachment  of  the  hook  of  the  lanyard.  The  outer  end  of  the 
tube  d  is  closed  over  the  flattened  end  of  the  wire,  which  is  bent 
over  into  a  hook,  as  shown,  and  serves  to  hold  the  wire  securely  in 

477 


478 


ORDNANCE  AND  GUNNERY. 


place  except  when  a  stout  pull  is  given  to  the  lanyard.  The  pull 
on  the  lanyard  straightens  out  the  hook  and  draws  the  serrated 
wire  through  the  friction  composition,  igniting  it.  The  fire  is 
communicated  to  the  rifle  powder  in  the  tube  6,  and  thence  through 
the  vent  to  the  powder  charge  in  the  gun. 

For  use  in  axial  vents,  in  order  to  prevent  the  primer  being 
blown  to  the  rear  among  the  men  of  the  gun  detachment,  a  coiled 
copper  wire  e  is  added  to  the  primer,  one  end  of  the  wire  being 


a 


FIG.  202. 


made  fast  to  the  top  of  the  primer  body,  the  other  end  to  the  loop 
for  lanyard  hook.  The  coil  is  extended  by  the  pull  of  the  lanyard, 
and  the  primer  when  blown  to  the  rear  remains  attached  to  the 
lanyard. 

Service  Primers. — The  primer  above  described  is  blown  out  of 
the  gun  by  the  explosion  of  the  powder  charge,  leaving  the  vent 
open  for  the  escape  of  gas.  This  disadvantage  is  overcome  in 
modern  practice  by  the  use  of  obturating  primers.  The  breech 
mechanisms  of  all  guns  now  made  are  adapted  to  obturating 
primers,  and  the  primer  just  described  is  no  longer  used  in  service 
cannon. 

The  firing  mechanism  described  in  the  chapter  on  guns,  page 
263,  is  fitted  to  most  of  the  cannon  in  our  service  that  do  not  use 
fixed  ammunition.  The  firing  mechanism  is  adapted  to  receive 
the  primer  and  hold  it  firmly,  and  is  provided  with  means  for 
firing  the  primer  either  by  the  pull  of  a  lanyard  or  by  electricity. 

276.  The  Service  Combination  Primer. — The  principal  primer 
used  in  our  service  is  a  combination  primer  which  is  arranged  to 


PRIMERS  AND  FUSE  FOR  CANNON. 


479 


be  fired  either  by  friction  or  by  electricity.     The  primer  is  shown 
complete  in  Fig.  203.    The  igniting  elements  are  shown  on  a  larger 


I  i     I     ill 
e  f  £hk 

FIG.  204. 


PIG.  203. 

scale  in  Fig.  204.  The  igniting  elements  are  assembled  in  the 
brass  case  /,  which  is  screwed  to  its  seat  in  the  primer. 

FRICTION  ELEMENTS. — For  firing  by  friction  there  is  pressed 
into  the  case  /  an  annular  pellet  of  friction  composition,  shown  in 
black  in  Fig.  204,  which  rests  on  a  vul- 
canite washer,  g.    The  washer  supports  the 
composition  and  prevents   it  from  crum- 
bling when  the  pull  which  fires  the  primer  is 
applied.     The  inner  end  of  the  firing  wire, 
k,  is  loosely  surrounded  by  the  serrated 
cylinder  h,  which  is  imbedded  up  to  the 
serrations  in  the  friction  composition.    The 

headed  inner  end  of  the  firing  wire  fits  in  a  seat  inside  the 
serrated  cylinder,  and  the  parts  are  held  securely  in  place  by  the 
forked  metal  support  e  and  the  closing  nut  6. 

When  the  firing  wire  is  pulled  the  serrated  cylinder  is  drawn 
through  the  composition  and  ignites  it.  The  conical  end  of  the 
cylinder  h  is  drawn  to  its  seat  in  the  rear  part  of , the  primer  and 
prevents  escape  of  gas  to  the  rear.  The  flame  from  the  friction 
composition  passes  through  vents  in  the  closing  nut,  6,  and  ignites 
the  priming  charge  of  compressed  and  loose  black  powder  in  the 
body  of  the  primer. 

The  mouth  of  the  primer  is  stopped  by  the  brass  cup,  a,  shel- 
lacked in  place.  This  cup  is  blown  out  by  the  explosion  of  the 
primer  charge,  and  the  flames  from  the  primer  pass  through  the 
vent  in  the  breech  block  and  ignite  the  powder  charge  in  the  gun. 
The  pellet  of  powder  near  the  mouth  of  the  primer  is  also  blown 
through  the  vent  and  insures  the  ignition  of  the  charge  in  the  gun. 


480  ORDNANCE  AND  GUNNERY. 

ELECTRIC  ELEMENTS. — For  electric  firing  the  wire  k  is  covered 
with  an  insulating  paper  cylinder  j  and  enters  the  primer  body 
through  a  vulcanite  plug  i.  The  wire  is  in  electric  contact  with 
the  serrated  cylinder  h,  Fig.  204,  but  this  is  insulated  from  the 
primer  body  by  the  vulcanite  washer  g  and  the  pellet  of  friction 
composition,  a  non-conductor  of  electricity. 

The  electrical  elements  of  the  primer  are  assembled  in  the 
metal  case  /.  The  head  of  the  forked  metal  support  e  is  in  contact 
with  the  headed  end  of  the  wire  k,  but  not  fastened  to  it.  The 
forked  end  of  the  support  is  held  in  the  vulcanite  cup  c.  The 
brass  contact  nut  6,  screwed  into  the  end  of  the  case  /,  presses  the 
assembled  parts  into  intimate  electrical  contact.  A  platinum  wire 
d  is  soldered  to  the  head  of  the  support  e  and  to  the  contact  nut  6. 
An  igniting  charge  of  guncotton  surrounds  the  wire. 

When  the  primer  is  inserted  in  the  gun  the  uninsulated  button 
at  the  end  of  the  wire  j  is  grasped  by  the  parts  of  an  electric  contact 
piece  through  which  the  electric  firing  current  passes.  The  cur- 
rent passes  through  the  wire  j,  the  platinum  bridge,  and  the  body 
of  the  primer  to  the  walls  of  the  gun  and  thence  to  the  ground. 

The  passage  of  the  electric  current  heats  the  platinum  wire, 
igniting  the  guncotton  and  the  priming  charge  of  powder. 

It  will  be  observed  that  the  friction  elements  of  the  combina- 
tion primer  are  independent  of  the  electrical  elements,  and  that 
when  one  of  these  primers  fails  to  fire  by  electricity  it  may  still  be 
fired  by  friction. 

If,  however,  the  primer  fails  in  an  attempt  to  fire  it  by  friction, 
it  will  not  generally  be  possible  to  fire  it  electrically  since  the 
cylinder  h,  which  has  been  pulled  into  the  head  of  the  primer,  is 
out  of  contact  with  the  part  e  and  the  platinum  wire  bridge.  The 
current  will  then  pass  directly  from  h  through  the  primer  body 
and  gun  to  the  ground. 

The  primer  should  in  this  case  be  at  once  removed  from  the 
vent  and  not  be  again  used. 

The  cuter  button  and  wire  k  may  be  turned  without  danger  of 
breaking  the  platinum  wire  bridge  d. 

When  an  electric  or  friction  primer  fails  to  fire  it  should  be 
removed  from  the  vent  and  the  wire  bent  down  and  around  the 
primer  to  prevent  attempts  to  use  it  again. 


PRIMERS  AND  FUSES  FOR  CAXNON. 


481 


The  metal  parts  of  the  primer  are  tinned  to  prevent  corrosion. 

Other  Friction  and  Electric  .Primers.— Primers  arranged  for 

firing  by  friction  alone  are  shown  in  Figs.  205  and  206.     The  primer 


FIG.  205. 


shown  in  Fig.  206,  of  simple  and  cheap  construction,  is  for  drill 
purposes  only. 


•*aiK         '             i     !  

n 

\mm-          .*f&*u^  —  ^n  

jjjll&j&l                   —  '                         j 

J 

FIG.  206. 
The  friction  primer  shown  in  Fig.  207  and  the  electric  primer 


FIG.  207. 

shown  in  Fig.  208  are  for  use  in  the  3.6-inch  and  7-inch  mortars, 


FIG.  208. 


The 


these   guns   not  being   provided  with   firing  mechanisms. 
primers  are  screwed  into  the  vents  in  the  breech  blocks. 

277.  Percussion  Primers.  —  The  friction  and  electric  primers 
described  are  used  in  guns  in  which  the  projectiles  and  powder 
charges  are  loaded  separately,  the  primer  being  separately  in- 
serted in  the  breech  block.  Percussion  primers,  and  the  electric 
primer  described  with  them,  are,  on  the  other  hand,  inserted  in 
cartridge  cases,  in  which  are  usually  assembled  both  the  projectile 
and  the  powder  charge. 


482  ORDNANCE  AND  GUNNERY. 

The  essential  parts  of  a  simple  percussion  primer  such  as  the 
cap  in  a  small  arm  cartridge,  are  the  primer  cup,  the  anvil,  and 
the  percussion  composition. 

Formerly  the  percussion  composition  of  all  service  primers 
contained  a  large  percentage  of  fulminate  of  mercury.  On  ac- 
count of  the  danger  involved  in  handling  mixtures  containing 
the  fulminate  of  mercury,  its  use  as  a  primer  ingredient  in  service 
primers  manufactured  at  the  Frankford  Arsenal  has  been  aban- 
doned, and  a  mixture  known  as  the  H-48  composition  is  now  em- 
ployed. 

This  mixture  contains  the  same  ingredients  as  the  friction  com- 
position, but  in  different  proportions,  as  follows : 

Chlorate  of  potash,  49.6.  Ground  glass,  16.6. 

Sulphide  of  antimony,  25.1.  Sulphur,  8.7. 

To  insure  the  practically  instantaneous  ignition  of  smokeless 
powder  charges,  the  addition  of  a  small  charge  of  quick-burning 
black  powder  is  required.  This  may  be  inserted  in  the  base  of  the 
smokeless  powder  charge,  or  may  be  contained  in  the  primer.  It 
is  desirable,  on  account  of  the  smoke  produced  by  black  powder 
and  the  fouling  of  the  bore,  that  the  quantity  of  black  powder 
used  be  limited  to  the  smallest  amount  that  will  produce  prompt 
and  complete  ignition  of  the  smokeless  powder.  The  minimum 
amounts  required  for  different  charges  have  been  determined  and, 
for  fixed  ammunition,  are  contained  in  the  percussion  and  igniting 
primers.  These  primers  are  inserted  in  the  head  of  the  cartridge 
case,  in  the  position  occupied  by  the  primer  in  the  small  arm 
cartridge. 

Two  sizes  of  percussion  primers,  the  110-grain  and  the  20- 
grain,  have  been  adopted  for  all  guns  from  the  1-pounder  to  the 
6-inch  Armstrong  inclusive. 

110-GRAiN  PERCUSSION  PRIMER. — The  body  /  is  of  brass,  2.93 
inches  long,  Fig.  209.  A  pocket  is  formed  in  the  head  of  the  case 
for  the  reception  of  the  metal  cup  e  containing  the  percussion  com- 
position d.  Projecting  up  from  the  bottom  of  the  pocket  is  the 
anvil  c  against  which  the  percussion  composition  is  fired.  Two 
vents  are  drilled  through  the  bottom  of  the  pocket.  The  priming 
charge  consists  of  110  grains  of  black  powder  inserted  under  high 


PRIMERS  AND  FUSES  FOR  CAXNON. 


483 


pressure  into  the  primer  body  around  a  central  wire.  The  with- 
drawal of  the  wire  after  the  compression  of  the  powder  leaves  a 
longitudinal  hole  the  full  length  of  the  primer.  Six  sets  of  radial 
holes  are  drilled  through  the  walls  of  the  primer  arid  through  the 
compressed  powder.  The  compression  of  the  powder  increases  the 
time  of  burning  of  the  priming  charge  and  causes  the  primer  to 
burn  with  a  torch-like  rather  than  an  explosive  effect,  making  the 


c     d  e  f 


FIG.  209. 


ignition  of  the  smokeless  powder  charge  more  complete.  The 
holes  through  the  priming  charge  increase  the  surface  of  com- 
bustion and  the  mass  of  flame,  and  direct  the  flames  to  different 
parts  of  the  charge  of  powder,  thus  facilitating  its  complete  igni- 
tion. The  paper  wad,  a,  shellacked  in  the  mouth  of  the  primer 
and  the  tin-foil  covering,  b,  serve  to  keep  out  moisture  and  to 
protect  the  primer  from  the  impact  of  the  powder  grains  when 
transported  assembled  in  cartridge  cases. 

This  primer  is   used   in    cartridge  cases  for  guns  from  the 
6-pounder  to  the  6-inch  Armstrong  gun,  inclusive. 

20-GRAiN  PERCUSSION  PRIMER. — The  20- 
grain  percussion  primer,  shown  in  Fig.  210, 
length  1.1  inches,  is  used  in  cartridge  cases  for 
1-pounder  subcaliber  tubes,  1-pounder  machine 
guns,  and  1.65-inch  Hotchkiss  guns. 

20-grain  Saluting  Primer. — This  primer,  Fig.  211,  costing  less 
to  manufacture  than  the  110-grain  primer,  is  to  be  used  in  place 
of  the  latter  with  blank  charges  only.  The 
primer  contains  a  charge  of  20  grains  of  loose 
rifle  powder.  As  black  powder  only  is  used 
in  blank  charges,  a  smaller  igniting  charge 
answers. 


FIG.  210. 


FIG.  211 


484 


ORDXAXCE  AND   GUNXERY. 


no-grain  Electric  Primer. — This  primer,  Fig.  212,  is  similar 
in  form  to  the  110-grain  percussion  primer  just  described,  and  has 

the  same  priming  charge  similarly  ar- 
ranged. Ignition  is  produced  electrically 
through  the  brass  cup  g,  to  which  one 
end  of  the  platinum  wire  e  is  soldered. 
A  small  quantity  of  guncotton  surrounds 
the  wire.  Electric  contact  is  made  with 
the  cup  g  by  the  insulated  firing  pin  of 
the  gun.  The  cup  is  insulated  from  the 
body  of  the  primer  by  the  cylinder  /  and 
bushing  d,  both  of  vulcanite.  The  brass 
contact  bushing  c,  to  which  the  other  end  of  the  platinum  wire 
is  soldered,  completes  the  electrical  connection. 

278.  Combination  Electric  and  Percussion  Primer. — In  Fig. 
213  is  shown  a  combination  electric  and  percussion  primer  used  in 
rapid-fire  guns  in  the  U.  S.  Navy.  Its 
construction  can  be  readily  understood 
from  the  figure.  The  insulation  is 
shown  by  the  heavy  black  lines.  When 
fired  by  percussion  the  percussion  cap 
s  not  directly  struck  by  the  firing  pin, 
but  by  the  point  of  a  plunger  forced  inward  by  the  blow. 

Igniting  Primers. — The  igniting  primers  are  for  use  in  car- 
tridge cases  for  subcaliber  tubes  for  seacoast  cannon  not  provided 
with  percussion  firing  mechanism.  They  contain  no  means  of 
ignition  within  themselves,  but  require  for  their  ignition  an  aux- 
iliary friction  or  electric  primer  which  is  inserted  in  the  vent  of  the 
piece  in  the  same  manner  as  for  service  firing.  The  flame  passes 
from  the  service  primer  through  the  vent  in  the  breech  block  to 
the  igniting  primer  in  the  head  of  the  cartridge  case.  The  flame 
from  the  service  primer  would  not  be  sufficient  to  ignite  properly 
the  smokeless  powder  charge  in  the  cartridge  case,  and  therefore 
the  igniting  primer  is  added. 

The  110-grain  and  the  20-grain  igniting  primers,  Figs.  214  and 
215,  differ  from  the  corresponding  percussion  primers  in  the  sub- 
stitution of  the  obturating  cup  a  and  obturating  valve  6,  both  of 
brass,  for  the  percussion  cup  and  anvil.  The  obturating  cup  a  is 


FIG.  213. 


PRIMERS  AND  FUSES  FOR  CAA'XON. 


485 


provided  with  a  central  vent  to  allow  passage  for  the  flame  from 
the  auxiliary  primer.  The  obturating  valve  b  is  cup-shaped,  and 
has  three  sections  of  metal  cut  away  from  its  top  and  sides  to 
allow  passage  of  the  flame.  The  valve  b  has  a  sliding  fit  in  the 
cup  a,  and  when  the  pressure  is  greater  in  front  of  the  valve  than 
behind  it,  the  valve  is  forced  to  the  rear  and  the  solid  top  of  the 
valve  closes  the  vent  in  the  outer  cup. 

The  valve  is  shown  in  section  in  Fig.  214,  in  the  position  it 
assumes  after  firing;  and  in  elevation  in  Fig.  215,  in  its  position 
before  firing. 


a 


FIG.  214. 


FIG.  215. 


Insertion  of  Primers  in  Cartridge  Cases. — The  percussion 
primers  and  igniting  primers  and  the  electrical  primers  of  the  same 
form  are  so  manufactured  as  to  have  a  driving  fit  in  their  seats  in 
the  cartridge  cases  to  which  they  are  adapted,  the  diameter  of  the 
primer  being  from  one-and-a-half  to  two  thousandths  of  an  inch 
greater  than  the  diameter  of  the  seat.  Special  presses  for  the  in- 
sertion of  the  primers  are  provided.  The  primer  must  not  be 
hammered  into  the  cartridge  case.  The  primer  seats  in  all  car- 
tridge cases  using  these  primers  are  rough  bored  to  a  diameter 
about  20  per  cent  less  than  the  finished  size,  and  then  mandreUed 
to  finished  dimensions  with  a  steel  taper  plug,  to  toughen  the  metal 
of  the  cartridge  case  around  the  primer  seat.  The  toughening  is 
necessary  to  prevent  expansion  of  the  primer  seats  under  pressure 
of  the  powder  gases,  and  consequent  loose  fitting  of  the  primers  in 
subsequent  firings. 


486  ORDXAXCE  AND  GUNXERY. 


FUSES. 

279.  Classification. — Fuses  are  the  means  employed  to  ignite 
the  bursting  charges  of  projectiles  at  any  point  in  the  flight  of  the 
projectile,  or  on  impact. 

They  are  of  three  general  classes: 
Time  fuses, 
Percussion  fuses, 
Combination  time  and  percussion  fuses. 

All  fuses  should  be  simple  in  construction,  safe  in  handling, 
certain  in  action,  and  not  liable  to  deterioration  in  store.  In 
addition  the  rate  of  burning  of  the  time  train  of  the  fuse  must  be 
uniform. 

The  time  fuse  alone,  that  is,  without  percussion  element,  is  no 
longer  used  in  modern  ordnance. 

Percussion  Fuses. — A  percussion  fuse  is  one  that  is  prepared 
for  action  by  the  shock  of  discharge,  and  that  is  caused  to  act  by 
the  shock  of  impact. 

When  ready  to  act,  as  after  the  shock  of  discharge,  the  fuse  is 
said  to  be  armed. 

Percussion  fuses  are  inserted  at  the  point  or  in  the  base  of  the 
projectile.  In  the  projectiles  for  1-  and  2-pounder  guns  the  fuse 
is  inserted  at  the  point.  The  percussion  fuses  for  field,  siege,  and 
seacoast  projectiles  are  base  insertion  fuses. 

The  percussion  fuse  consists  essentially  of  the  case  or  body,  of 
brass,  which  contains  and  protects  the  inner  parts  and  affords  a 
means  of  fixing  the  fuse  in  the  projectile;  the  plunger,  carrying 
the  firing  pin  and  provided  with  devices  to  render  the  fuse  safe  in 
handling;  the  percussion  composition,  which  is  fired  by  the  action 
of  the  plunger  on  impact;  and  the  priming  charge  of  black  gun- 
powder. 

The  percussion  composition  of  all  service  fuses  manufactured 
at  Frankford  Arsenal  is  the  same.  The  ingredients  are  chlorate  of 
potash,  sulphide  of  antimony,  sulphur,  ground  glass,  and  shellac. 
The  thoroughly  pulverized  ingredients  are  mixed  dry,  and  alcohol 
is  added  to  dissolve  the  shellac.  The  percussion  pellets  are  formed 
by  pressing  the  mixture  while  in  a  plastic  state  into  the  percussion- 


PRIMERS  AXD  FUSES  FOR  CAXXON. 


487 


primer  recess.  Upon  the  evaporation  of  the  alcohol  the  shellac 
causes  the  pellet  to  adhere  to  the  metal  of  the  recess. 

A  fulminate  of  mercury  percussion  composition  Mras  formerly 
used  in  fuse  primers,  but  on  account  of  the  danger  incident  to 
handling  this  compound  it  has  been  abandoned  as  a  primer  in- 
gredient. 

It  is  still  used  abroad,  and  the  percussion  composition  of  both 
the  Ehrhardt  and  Krupp  combination  time  and  percussion  fuses 
contains  fulminate  of  mercury. 

Point  Percussion  Fuse. — Point  percussion  fuses  are  adapted 
to  the  projectiles  for  1-pounder  and  2-pounder  guns  only. 


a 


FIG.  216. 

The  body,  a  Fig.  216,  is  of  brass.  The  percussion  composition 
and  the  priming  charge  of  black  powder  are  assembled  in  a 
vented  case,  e,  which  is  screwed  into  a  recess  formed  in  the  head  of 
the  fuse.  A  thin  brass  disk,  the  primer  shield,  protects  the  per- 
cussion composition  from  the  firing  pin  in  the  bod}^  of  the  fuse.  It 
prevents  any  dislodgment  of  the  composition  during  transporta- 
tion or  by  shock  of  discharge  and  also  restrains  the  firing  pin  during 
the  flight  of  the  projectile. 

Contained  in  the  body  of  the  fuse  is  the  plunger,  which  consists 
of  the  firing  pin  j,  the  cylindrical  sleeve  h,  and  the  split-ring  spring  k, 
all  of  brass.  The  firing  pin  has  an  enlarged  rear  part  joined  to  the 
forward  part  by  a  conical  slope  and  provided  near  the  bottom 
with  a  groove,  /,  of  diameter  slightly  larger  than  the  diameter  of 
the  forward  part  of  the  pin.  A  radial  hole,  i,  through  the  pin  near 


488  ORDNANCE  AXD  GUNNERY. 

its  forward  end,  and  an  axial  hole  from  this  point  to  the  rear  end 
of  the  pin,  provide  a  passage  for  the  flame  from  the  priming  charge. 
The  rear  part  of  the  bore  through  the  sleeve  A  is  of  diameter  just 
sufficient  to  admit  the  spilt  ring  which  rests  against  the  forward 
shoulder  of  the  counterbored  recess  in  the  sleeve  and  holds  the 
firing  pin  so  that  its  point  is  wholly  within  the  sleeve.  The  front 
part  of  the  sleeve  is  counterbored  to  permit  ready  entrance  of  the 
flame  from  the  priming  charge  into  the  passage  through  the  filing 
pin.  The  plunger  thus  assembled  is  placed  hi  the  fuse  body, 
which  is  closed  by  the  brass  closing  screw  m  provided  with  a  cen- 
tral vent  which  is  in  turn  closed  by  the  brass  disk  n.  To  prevent 
pressure  of  the  closing  screw  on  the  plunger,  which  might  cause 
expansion  of  the  split  ring  and  the  arming  of  the  fuse,  the  plunger 
is  allowed  a  longitudinal  play  in  the  fuse  body  of  from  one  to  two 
hundredths  of  an  inch.  With  the  parts  of  the  fuse  in  this  position 
the  point  of  the  firing  pin  is  prevented  from  coming  into  contact 
with  the  percussion  composition,  and  therefore  the  fuse  cannot  be 
fired. 

If  sufficient  force  is  applied  rearwardly  to  the  sleeve  h,  the  split 
ring  k  will  be  forced  over  the  enlarged  portion  of  the  firing  pin  until 
it  rests  in  the  groove  I  near  the  bottom;  and  the  sleeve,  moving  to 
the  rear,  will  expose  the  point  of  the  firing  pin.  The  fuse  is  then 
armed,  as  shown  in  Fig.  217. 

To  insure  arming  of  the  fuse  when  fired  the  resistance  of  the 
split  ring  to  expansion  is  made  less  than  the  force  necessary  to 
give  the  sleeve  the  maximum  acceleration  of  the  projectile.  There- 
fore when  the  piece  is  fired  and  while  the  projectile  is  attaining  its 
maximum  acceleration,  the  pressure  of  the  sleeve  will  force  the 
ring  over  the  enlarged  part  of  the  firing  pin  into  the  groove  at  the 
rear. 

The  diameter  of  this  groove  being  greater  than  the  diameter  of 
the  front  part  of  the  firing  pin,  the  ring  is  now  expanded  into  the 
counterbored  recess  in  the  sleeve  and  locks  the  sleeve  and  firing 
pin  together,  with  the  point  of  the  firing  pin  projecting  beyond  the 
sleeve. 

As  the  plunger  of  the  fuse  does  not  encounter  the  atmospheric 
resistance  which  retards  the  projectile  in  its  flight,  it  is  probable 
that  during  the  flight  of  the  projectile  the  plunger  moves  slowly 


PRIMERS  AND  FUSES  FOR  CANNON. 


489 


a 


forward  until  the  point  of  the  firing  pin  rests  against  the  brass 
primer  shield. 

At  impact  of  the  projectile  the  combined  weight  of  the  plunger 
parts  acts  to  force  the  point  of  the  firing  pin  through  the  primer 
shield  and  into  the  percussion  composition,  igniting  the  composi- 
tion. 

The  flame  from  the  priming  charge  passes  through  the  forward 
vents,  through  the  passages  in  the  plunger,  and  through  the  vent 
in  the  closing  screw,  blowing  out  the  closing  disk  and  igniting  the 
bursting  charge  in  the  shell. 

280.  Base  Percussion  Fuse,  for  minor  caliber  shell.  This 
fuse,  as  well  as  the  point  percussion  fuse,  is  adapted  to  the  pro- 
jectiles for  1-pouncler  and  2-pounder  guns.  The  fuse  for  the  pro- 
jectiles of  the  6-pounder  gun  and  of  the  2.38-inch  field  gun  is 
similar  in  construction. 

The  fuse,  Fig.  218,  is  similar  in  construction  and  action  to  the 
point  percussion  fuse.  As  the  primed  end  of  the  fuse  is  toward  the 
interior  of  the  shell  the  flame  from  the  priming 
charge  passes  directly  to  the  bursting  charge  in 
the  shell  without  passing  through  the  body  of 
the  fuse.  The  flame  passages  through  the 
plunger  parts  are  therefore  omitted.  The  pri- 
mer cup  6,  containing  the  percussion  composi- 
tion and  priming  charge,  is  closed  at  its  outer 
end  by  the  brass  disk  a,  which  is  secured  in 
place  by  crimping  over  it  a  thin  wall  left  on  the 
brass  closing  cap  screw  c. 

The  act  of  arming  a  ring-resistance  percus-  FlG-  218- 

sion  fuse  shortens  the  plunger  and  increases  materially  its  longitu- 
dinal play  in  the  fuse  body.  This  fact  permits  a  ready  and  simple 
means  of  inspecting  for  premature  arming  without  dismantling  the 
fuse.  If  the  fuse  be  held  close  to  the  ear  and  shaken,  the  marked 
difference  between  the  play  of  the  plunger  in  an  armed  fuse  and  in 
an  unarmed  one  can  be  readily  discerned. 

Centrifugal  Fuses. — The  centrifugal  fuse  of  service  pattern  is 
the  result  of  a  long  series  of  experiments  made  for  the  purpose  of 
developing  a  fuse  that  would  fulfill  the  requirements  of  absolute 
safety  in  handling  and  transportation,  and  certainty  of  action. 


490  ORDNANCE  AND  GUNNERY. 

In  the  case  of  ring-resistance  fuses,  or  any  fuse  the  action  of 
which  depends  on  the  longitudinal  stresses  developed  by  the  pres- 
sure in  the  gun,  the  conditions  of  safety  in  handling  and  certainty 
of  action  are  opposing  ones. 

It  was  impossible  to  meet  successfully  both  sets  of  conditions 
in  all  cases,  the  stress  developed  in  the  direction  of  the  axis  by 
accidental  dropping  of  a  fuse  being  in  many  cases  higher  than  that 
developed  in  the  gun. 

A  fuse  which  is  armed  by  the  centrifugal  force  developed  by  the 
rotation  of  the  projectile,  and  which  is  safe  until  the  maximum 
velocity  of  rotation  is  nearly  attained,  has  been  developed  at  the 
Frankford  Arsenal  and  is  now  used  in  the  projectiles  for  low 
velocity  guns;  the  mountain  gun,  and  all  howitzers  and  mortars. 
In  these  guns  the  maximum  acceleration  of  the  projectile  in  the 
bore  is  so  low  that  the  ring-resistance  fuse  must  be  very  sensitive 
in  order  to  insure  arming,  with  the  result  that  it  becomes  too  sen- 
sitive foT  safety  in  handling  and  transportation.  For  the  projec- 
tiles of  other  guns  the  fuses  are  similar,  but  are  provided  with  ring- 
resistance  plungers  instead  of  centrifugal  plungers. 

The  centrifugal  fuse,  before  arming,  is  shown  in  Fig.  219. 
Fig.  220  is  a  view  of  the  plunger  after  arming. 

The  fuse  body,  or  stock,  and  the  primer  parts  of  the  centrifugal 
fuse  do  not  differ  materially  from  the  corresponding  parts  of  the 
ring-resistance  fuses.  To  better  protect  the  priming  charge  the 
closing  cap  screw  b  is  lengthened  and  the  vented  primer-closing 
screw  a  is  added. 

The  body  of  the  centrifugal  plunger  is  in  two  parts,  nearly  semi- 
cylindrical  in  shape,  wrhich  when  the  fuse  is  at  rest  are  held  to- 
gether by  the  pressure  of  a  spiral  spring  g  contained  in  the  cylin- 
drical bushing  e  which  is  secured  to  one  of  the  plunger  halves.  The 
spring  exerts  its  pressure  on  the  other  half  of  the  plunger  through 
the  bolt  /.  Pivoted  in  a  recess  in  one  half  of  the  plunger  is  the 
firing  pin  d,  which  when  the  fuse  is  at  rest  is  held  with  its  point 
below  the  front  surface  of  the  plunger  by  the  lever  action  of  the 
link  c  which  is  pivoted  in  the  other  half.  Under  the  action  of  the 
centrifugal  force  developed  by  the  rapid  rotation  of  the  projectile 
the  two  halves  of  the  plunger  separate.  The  separating  move- 
ment causes  the  rotation  of  the  firing  pin  d,  the  point  of  which  is 


PRIMERS  AND  FUSES  FOR  C A XX OX. 


491 


now  held  in  advance  of  the  front  surface  of  the  plunger,  Fig.  220, 
ready,  on  impact  of  the  projectile,  to  pierce  the  brass  primer 
shield  and  ignite  the  percussion  composition.  When  the  fuse  is 
armed  the  end  of  the  link  c  rests  on  the  pivot  of  the  firing  pin, 
thus  affording  support  to  the  firing  pin  when  it  strikes  the  per- 
cussion primer.  The  separation  of  the  plunger  parts  is  limited  by 
the  nut  i  coming  to  a  bearing  on  a  shoulder  in  the  bushing  e,  so 


FIG.  219. 


FIG.  220. 


FIG.  221. 


as  not  to  permit  the  diameter  of  the  expanded  plunger  to  equal 
the  interior  diameter  of  fuse  stock,  see  Fig.  222. 

A  rotating  piece,  h  Figs.  219  and  221,  screwed  into  head  of  fuse 
stock,  engages  in  a  corresponding  slot  cut  through  the  bottom 
of  both  plunger-halves  and  insures  rotation  of  the  plunger  with  the 
shell. 

The  strength  of  the  spring  g  is  so  adjusted  that  the  fuse  will 
not  arm  until  its  rapidity  of  revolution  is  a  certain  percentage  of 
that  expected  in  the  shell  in  which  it  is  to  be  used,  and  that  it  will 
certainly  arm  when  the  rapidity  of  revolution  approximates  that 
expected  in  the  shell.  Should  the  parts  of  the  plunger  be  acci- 
dentally separated  and  the  fuse  armed  by  a  sudden  jolt  or  jar  in 
transportation  or  handling,  the  reaction  of  the  spring  will  imme- 
diately bring  the  plunger  to  the  unarmed  condition. 

The  fuse  just  described  is  called  the  F  fuse. 


492 


ORDNANCE  AND  GUNNERY. 


FIG.  222. 


The  fuse  shown  in  Fig.  222,  the  S  fuse,  is  for  use  with  3.6-  and 
7-inch  mortar  shell,  powder-charged.  The  additional  priming 

in  end  of  fuse  gives  a  greater  body  of 
flame  than  is  emitted  from  the  F  fuse. 

A  similar  fuse  of  larger  size  is  used 
in  powder-charged  shell  of  8-inch  caliber 
and  over. 

A  fuse,  called  the  12  M  fuse,  is  pro- 
vided for  use  in  the  12-inch  mortar  deck- 
piercing  and  torpedo  shell.  This  fuse  is 
similar  in  construction  to  the  other 
centrifugal  fuses,  but  on  account  of  the 
low  velocity  of  rotation  of  mortar  pro- 
jectiles and  their  low  striking  velocity 
a  much  heavier  plunger  is  needed  to 
provide  the  force  necessary  for  arming 
the  fuse,  and  for  puncturing  the  primer- 
shield  on  impact. 

281.  Combination  Time  and  Per- 
cussion Fuses. — All  combination  fuses  used  in  the  service  are  point 
insertion  and  combine  the  elements  of  time  and  percussion  ar- 
ranged to  act  independently  in  one  fuse  body. 

Combination  fuses  contain  two  plungers  and  two  primers. 
One  plunger,  the  time  plunger,  is  armed  by  the  shock  of  discharge 
and  fires  its  primer  immediately,  igniting  the  time  train  of  the 
fuse.  The  other  plunger,  the  percussion  plunger,  is  also  armed  by 
the  shock  of  discharge  but  fires  its  primer  on  impact  of  the  pro- 
jectile. 

Service  Combination  Fuse. — The  upper  part  of  the  fuse,  Fig. 
223,  contains  the  time  elements,  the  lower  part  the  percussion  ele- 
ments. The  time  elements  consist  of  the  concussion  or  time 
plunger  6,  the  firing  pin  c,  and  the  time  train.  The  firing  pin  is 
fixed  in  the  body  of  the  fuse,  and  the  plunger  carries  the  percus- 
sion composition  and  a  small  igniting  charge  of  black  powder. 
The  plunger  is  held  out  of  contact  with  the  firing  pin  by  the  split 
resistance-ring  a.  On  the  shock  of  discharge  the  inertia  of  the 
plunger  acting  through  the  conical  surface  in  contact  with  the 
split  ring  expands  the  ring  so  that  the  plunger  can  pass 


PRIMERS  AND  FUSES  FOR  CANNON 


493 


through  it  and   carry  the  percussion   composition   to   the   firing 
pin. 

The  time  train  of  the  fuse  is  composed  of  two  rings  of  powder, 
/  and  h,  contained  in  grooves  cut  in  the  two  time-train  rings  m 
and  n.  The  grooves  are  not  cut  completely  around  the  rings,  but 
a  solid  portion  is  left  between  the  ends  of  the  groove  in  each  ring. 


FIG.  223. 

Mealed  powder  is  compressed  into  the  grooves  under  a  pressure  of 
70,000  pounds  per  square  inch,  forming  a  train  7  inches  long,  the 
combined  length  of  the  two  grooves. 

The  flajne  from  the  percussion  composition  passes  through 
the  vent  d,  igniting  the  compressed  tubular  powder  pellet  e,  which 
in  turn  ignites  one  end  of  the  upper  time  train  /.  "When  the  fuse  is 
set  at  zero  the  flame  passes  immediately  from  the  upper  time  train 
through  the  powder  pellet  g  to  one  end  of  the  lower  time  train  h; 
thence  through  the  pellet  i  and  vent  /  to  the  powder  k  in  the  an- 
nular magazine  at  the  base  of  the  fuse. 

Under  each  of  the  time  rings  is  a  felt  Washer,  o  and  p,  that 
closes  the  joint  under  the  ring  against  the  passage  of  flams,  except 
through  the  hole  in  the  washer  directly  over  the  vent  in  the  part 
below.  The  upper  washer  o  is  glued  to  the  upper  corrugated  sur- 
face of  the  lowrer  time  ring  n  and  moves  with  that  ring.  The  lower 
wrasher  p  is  glued  to  the  fuse  body  and  is  stationary.  The  upper 


494 


ORDNANCE  AND  GUXNERY. 


time  ring  m  is  fixed  in  position  by  two  pins  I  halved  into  the  fuse 
body  and  the  ring.  The  lower  time  ring  is  movable,  and  any  of 
the  graduations  on  its  exterior,  see  Fig.  224,  which  correspond  to 


\ 


S 


FIG.  224. 

seconds  and  fifths  of  seconds  of  burning,  may  be  brought  to  the 
datum  line  marked  on  body  of  fuse  below  the  ring.  The  ring  is 
moved,  in  setting,  by  means  of  a  wrench  applied  to  the  projecting 
stud  w. 

To  set  the  fuse  for  any  time  of  burning,  say  20  seconds,  move 
the  lower  time  ring  n  until  the  mark  20  is  over  the  datum  line. 
On  ignition  of  the  primer  the  flame  ignites  the  upper  time  train  /, 
which  burns  clockwise,  looking  from  base  to  point  of  fuse,  until 
the  hole  through  the  washer  over  the  zero  mark  of  the  lower  ring 
n  is  encountered.  The  flame  then  passes  through  the  vent  g  to 
the  lower  time  train  n,  which  burns  anti-clockwise  until  the  mark 
20  is  reached.  This  mark  being  over  the  vent  i  in  the  body  of 
fuse,  the  flame  now  passes  to  the  magazine  k.  The  setting  of  the 
fuse  consists  in  fixing  the  position  of  the  passage  from  the  upper 
to  the  lower  time  train,  so  as  to  include  a  greater  or  less  length 
of  each  train  between-  the  vent  e  and  the  vent  i. 

In  each  time  ring  a  vent  opens  from  the  initial  end  of  the 
powder  train  to  the  exterior.  The  vent  contains  a  pellet  of  pow- 
der and  is  covered  by  a  thin  brass  cup.  The  vent  in  the  lower 


PRIMERS  AND  FUSES  FOR  CANNON.  495 

time  ring  is  seen  at  x  in  Fig.  223.  The  caps,  x,  of  both  vents  are 
shown  in  Fig.  224.  The  blowing  out  of  the  cap  affords  a  passage 
to  the  open  air  for  the  flame  from  the  burning  time  train,  thus 
preventing  the  bursting  of  the  fuse  by  the  pressure  of  the  con- 
tained gases. 

When  the  fuse  is  set  at  safety,  indicated  by  the  letter  S  stamped 
on  the  lower  time  ring,  the  position  shown  in  Fig.  224,  the  solid 
metal  between  the  ends  of  the  upper  time  train  is  over  the  vent  g 
to  the  lower  train,  and  the  solid  metal  between  the  ends  of  the 
lower  train  is  over  the  vent  i  leading  to  the  magazine.  Tn  case  of 
accidental  firing  by  the  time  plunger,  the  upper  train  will  be  com- 
pletely consumed  without  communicating  fire  to  the  lower  train 
and  to  the  magazine.  The  fuse  is  habitually  carried  at  this  setting, 
which  serves  also  when  it  is  desired  to  explode  the  shell  by  impact 
only. 

For  percussion  firing  the  fuse  is  now  provided  with  a  ring- 
resistance  plunger  similar  to  that  shown  in  Fig.  218.  Better 
results  are  obtained  with  the  ring-resistance  plunger  than  with  the 
centrifugal  plunger,  which  was  formerly  used  in  these  fuses  and 
is  shown  at  r  in  Fig.  223.  A  vent  s  leads  from  the  percussion 
primer  to  the  annular  magazine  k.  A  thin  brass  cap  t  separates 
the  lower  plunger-recess  from  the  powder  in  the  four  radial  cham- 
bers v  cut  in  the  bottom  closing  screw.  The  central  vent  in  the 
closing  screw  is  closed  by  a  piece  of  shellacked  linen,  held  in  place 
by  a  brass  washer. 

These  fuses  are  issued  fixed  in  the  loaded  projectiles.  For 
protection  in  transportation  the  fuse  is  covered  by  a  spun  brass 
cap,  soldered  on  to  the  head  of  the  projectile.  The  soldering  strip 
is  torn  off  and  the  cover  removed  before  using  the  projectile. 

A  21-second  fuse  of  this  pattern  is  now  in  service,  and  a  31- 
second  fuse  is  being  developed. 

282.  COMBINATION  FUSE,  OLD  PATTERN. — As  the  former  model 
of  combination  fuse  may  perhaps  still  be  encountered  in  sendee, 
it  is  illustrated  here.  The  time  train,  b  Fig.  225,  is  made  by 
filling  a  lead  tube  with  mealed  powder  and  then  drawing  the  filled 
tube  through  dies  until  its  diameter  has  been  reduced  to  the  de- 
sired dimension.  The  powder  train  is  thereby  given  practically 
uniform  density,  so  that  it  burns  more  uniformly  than  the  time 


496 


ORDNAXCE  AND  GUNNERY. 


trains  of  previous  fuses.    The  results,  however,  were  not  so  good 
as  the  results  obtained  with  fuses  of  the  present  service  model. 

The  time  train,  b,  incased  in  the  lead  tube,  is  wound  spirally 
around  the  lead  cone  c.  To  set  the  fuse  for  any  time  of  burning 
the  time  train  and  lead  cone  are  punctured,  by  means  of  a  tool 
provided  for  the  purpose,  at  the  point  on  the  scale  marked  on  the 
cover  of  fuse  corresponding  to  the  time  of  burning  desired.  The 
puncture  passes  completely  through  the  time  train  and  the  lead 
cone  behind  it,  forming  a  channel  from  the  annular  space  in  which 


FIG.  225. 


the  letter  b  appears  to  the  powder  in  the  time  train.  When  the 
projectile  is  fired  the  flame  from  the  percussion  composition  ignites 
the  compressed  powder  ring  d,  and  the  flame  from  this  ring  ignites 
the  time  train  at  the  point  at  which  it  has  been  punctured.  The 
safety  pin  a  retains  the  time  plunger  in  its  unarmed  position,  and 
must  be  withdrawn  before  placing  the  projectile  hi  the  gun. 

Two  fuses  of  this  pattern  were  made,  one  with  a  15-second  time 
train  and  the  other  with  a  28-second  time  train. 


PRIMERS  AND  FUSES  FOR  CANNON. 


497 


EHRHARDT  COMBINATION  FUSE. — This  fuse  is  similar  in  con- 
struction to  the  Frankford  Arsenal  fuse,  latest  pattern,  described 
above  and  differs  only  in  details. 

The  arming  of  the  time  plunger  of  the  Ehrhardt  fuse,  Fig.  226, 
is  resisted  by  the  U-shaped  spring  a,  the  upper  ends  of  which  are 
sprung  out  into  a  counterbored  recess  in  the  closing  cap,  and  by 


FIG.  226. 

the  slender  brass  pin  6,  which  passes  through  the  plunger  and 
both  sides  of  the  closing  cap.  At  discharge  of  the  piece  the  inertia 
of  the  plunger  shears  the  pin  b  and  straightens  the  U-shaped 
spring  a,  permitting  the  plunger  to  strike  the  firing  pin. 

In  the  percussion  mechanism  the  composition  is  carried  in  the 
plunger  and  the  firing  pin  is  fixed  in  the  diaphragm  d  in  body  of 
fuse.  The  plunger  is  held  away  from  the  firing  pin,  before  firing, 
by  the  brass  restraining  pin  c.  The  pin  is  let  into  a  hole  in  the 
diaphragm  d,  the  head  of  the  pin  abutting  against  a  shoulder  near 
the  bottom  of  the  hole.  The  restraining  pellet  of  powder  e  is 
pressed  in  to  fill  the  recess  above  the  pin.  A  perforated  brass 
disk  and  a  piece  of  linen  close  the  hole  at  its  upper  end  and  pre- 
vent the  powder  pellet  from  being  jarred  out  of  place.  The  burn- 


498 


ORDXA.VCE  AND  GUXXERY. 


ing  of  this  pellet  on  ignition  from  the  time  plunger  leaves  the 
restraining  pin  and  percussion  plunger  free  to  move  forward  at 
impact. 

A  compressed  charge  of  black  powder,  g,  is  inserted  into  the 
extension  of  the  closing  screw  /  to  reinforce  the  magazine  charge 
and  effectually  to  carry  the  flame  to  the  base  charge  in  the  shrapnel. 

The  Krupp  combination  fuse  does  not  differ  essentially  from  the 
Ehrhardt  fuse.  The  shear  pin  through  time  plunger  is  omitted, 
the  U-shaped  spring  being  made  strong  enough  to  offer  sufficient 
resistance  against  accidental  arming.  The  percussion  plunger, 
carrying  the  percussion  composition,  is  held  away  from  the  firing 
pin,  before  firing,  by  a  sleeve  and  an  inverted  U-shaped  resistance 
spring.  A  spiral  spring  between  plunger  and  firing  pin  prevents 
the  creeping  forward  of  the  plunger  during  the  flight  of  the  pro- 
jectile. 

Detonating  Fuses. — These  fuses  are  for  use  hi  shell  containing 
high  explosives. 


-4.29- 


FIG.  227. 

Fig.  227  shows  the  form  of  detonating  fuse  for  point  insertion 
in  field  shell.  Fig.  228  shows  the  form  of  fuse  for  base  insertion 
in  siege  and  seacoast  projectiles. 


FIG.  228. 


In  order  to  prevent  the  unscrewing  of  the  fuse  during  flight  of 
the  projectile,  all  point  insertion  fuses  are  provided  with  right- 


PRIMERS  AND  FUSES  FOR  CAXNON. 

t 

handed  screw  threads  and  base  insertion  fuses  with  left-handed 
threads. 

283.  The  Fuse  Setter. — The  fuse  setter  is  a  device  for  the 
rapid  and  accurate  setting  of  the  time  fuse  in  the  field  gun  pro- 
jectile. It  is  attached  to  a  hinged  bracket  on  the  caisson  for  the 
field  gun,  see  Fig.  122,  in  a  position  convenient  for  the  cannoneer 
who  serves  the  caisson. 

The  base  of  the  fuse  setter,  Fig.  229,  is  fixed  to  the  bracket  on 
the  caisson.  Mounted  on  the  base  are  two  movable  rings  called 
the  corrector  ring  and  range  ring.  The  range  ring  carries  the 
range  scale  graduated  in  yards,  and  the  corrector  ring  carries  an 
index  or  pointer  that  moves  between  the  corrector  scales  that  are 
fastened  to  the  fixed  cover.  The  base  and  the  two  rings  are  bored 
out  conically  to  fit  over  the  combination  time  and  percussion  fuse 
used  in  the  3-inch  projectile.  The  corrector  ring  is  notched  to 
receive  the  rotating  stud,  w  Fig.  224,  which  projects  from  the 
time  train  ring  of  the  fuse.  A  spring  plunger  projects  inwardly 
from  the  range  ring  of  the  fuse  setter. 

A  guide  fixed  to  the  base  serves  to  direct  the  point  of  the  pro- 
jectile into  the  socket  of  the  fuse  setter  and  to  support  the  car- 
tridge during  the  operation  of  fuse  setting. 

To  set  the  fuse  for  the  time  of  burning  corresponding  to  any 
range,  as  1000  yards,  the  range  ring  is  turned  by  means  of  the 
range-worm  handle  until  the  1000  mark  on  the  range  scale  is 
opposite  the  datum  line  marked  on  the  corrector  scale,  see  Fig. 
229.  The  weather-proof  cover  of  the  time  fuse  in  the  projectile  is 
stripped  off  and  the  point  of  the  projectile  is  then  placed  in  the 
fuse  setter,  the  rotating  stud  on  the  fuse  engaging  in  the  notch  in 
the  corrector  ring.  The  cartridge  is  then  turned  slowly  in  a  clock- 
wise direction  until  the  spring  plunger,  which  has  been  pushed  in 
by  the  insertion  of  the  fuse  in  the  fuse  setter,  is  forced  out  into  a 
notch  prepared  for  it  in  the  body  of  the  fuse.  The  plunger  pre- 
vents further  rotation  of  the  cartridge,  the  time  fuse  of  which  has 
now  been  set  to  the  proper  time  of  burning  for  1000  yards. 

The  rate  of  burning  of  different  fuses  of  the  same  lot  will  be 
uniform,  but  it  may  vary  slightly  from  the  rate  of  burning  used  in 
the  graduation  of  the  scale  of  the  fuse  setter.  This  must  be  deter- 
mined by  actual  firings,  and  if  after  a  few  shots  it  is  found  that 


500 


ORDNANCE  AND  GUNXERY. 


the  projectiles  burst  short  of  or  beyond  the  range  for  which  the 
time  fuse  is  set,  or  if  the  height  of  burst  is  not  exactly  as  desired, 


•  Cbrrvcfor  fndejc 
Sbr rector  Scales 


— Corrector  Worm 
—Notch  foe  delating  Pin  of  fuze 


> Stamping  Salts 


FIG.  229. — Fuse  Setter  for  3-inch  Projectiles. 

a  correction  is  made  in  the  setting  of  the  fuse  by  means  of  the 
corrector  ring  in  the  fuse  setter. 

The  height  of  burst  may  be  increased  or  diminished  by  turning 


PRIMERS  AND  FUSES  FOR  CANNON.  501 

the  corrector  ring,  by  means  of  the  corrector-worm  thumb  nut 
to  increase  or  diminish  the  corrector  scale  reading. 

A  point  on  the  corrector  scale  corresponds  to  a  difference  of 
one  mil  hi  the  height  of  burst. 

The  fuse  setters  now  issued  are  provided  with  two  corrector 
scales,  one  for  use  with  Frankford  Arsenal  and  Krupp  fuses,  and 
the  other  for  use  with  Ehrhardt  fuses. 

284.  Arming  Resistance  of  Fuse  Plungers.  RIXG  RESIST- 
ANCE FUSES. — The  arming  resistance  of  the  ring  resistance  fuse, 
Fig.  216,  is  the  resistance  offered  by  the  split  ring  k  to  movement 
over  the  enlarged  base  of  the  firing  pin. 

As  the  projectile  is  accelerated  in  the  bore  of  the  gun  the  split 
ring  imparts  the  acceleration  to  the  sleeve  h  of  the  plunger.  If 
the  resistance  that  the  split  ring  offers  to  rearward  motion  over 
the  slope  of  the  firing  pin  is  less  than  the  pressure  that  the  ring 
must  impart  to  the  sleeve  to  give  to  the  sleeve  the  maximum 
acceleration  of  the  projectile,  the  rearward  movement  of  the  ring 
will  occur  and  the  fuse  will  arm. 

Problem  1.  Determine  the  maximum  permissible  arming  re- 
sistance for  the  ring-resistance  fuse  in  the  projectile  for  the  3-inch 
gun,  for  which  we  have  the  following  data. 

Maximum  pressure,  P  =  33,000  Ibs.  per  sq.  in. 

Weight  of  projectile,  w  =  151bs. 

Weight  of  plunger  sleeve,  ic8=4Q4  grains  =  464/7000  Ibs. 
Diameter  of  projectile,        d  =  3  inches. 

Neglecting  friction  and  the  rotation  of  the  projectile  we  will 
assume  that  the  pressure  is  wholly  employed  in  giving  motion  of 
translation  to  the  projectile. 

The  maximum  acceleration  of  the  projectile  is 

g     xffi    32.16X33000X^X9 
a  =  wPT"  15X4 

If  the  split  ring  of  the  fuse  plunger  imparts  this  acceleration  to 
the  sleeve,  the  pressure  on  the  ring  will  be 

w.    500120X464 

P0unds 


502  ORDNANCE  AND  GUNXEKY. 

Therefore  the  plunger  with  sleeve  weighing  464  grains  will  arm  in 
the  gun  if  the  arming  resistance  of  the  fuse  is  anything  less  than 
1030.8  pounds. 

285.  Problem  2.  The  actual  arming  resistance  of  the  fuse  for 
the  3-inch  projectile  is  220  pounds.     What  pressure  per  square 
inch  is  required  in  the  gun  in  order  to  arm  the  fuse? 

Equating  the  values  of  a  in  the  equations  established  in  the 
preceding  problem,  and  writing  p  for  P  to  indicate  any  pressure 
per  square  inch,  we  obtain 

*d?^_F_ 
^  4  w    wa 

The  total  pressure  on  the  projectile  at  any  instant  divided  by 
the  weight  of  the  projectile  is  equal  to  the  pressure  on  the  sleeve 
at  the  instant  divided  by  the  weight  of  the  sleeve. 

Making  F  =  220,  and  substituting  for  the  other  quantities  the 
values  as  given  in  the  preceding  problem,  we  find 

4X15X220X7000 
P=        .X9X464        =<0431bs.persq.in. 

The  fuse  will  arm  under  any  pressure  in  excess  of  this. 
Problem  3.  What  is  the  minimum  effective  powder  pressure 
that  will  arm  the  ring-resistance  fuse  described  below,  when  fired 
from  the  6-inch  gun? 

Weight  of  projectile,  w  =  1061bs. 

Weight  of  plunger  sleeve,  ws  =  700  grains  ==0.1  Ibs. 

Ring  resistance  to  arming,     =220  Ibs. 

Ans.  p  =  8248  Ibs.  per  sq.  in. 

286.  CENTRIFUGAL  FUSE. — The  arming  resistance  of  the  cen- 
trifugal fuse,  Fig.  219,  is  the  pressure  exerted  by  the  spring  g, 
which  holds  the  plunger  halves  together.     The  centrifugal  force 
due  to  the  rotation  of  the  projectile  tends  to  separate  the  plunger 
halves.     In  order  that  the  fuse  may  be  armed  when  the  projectile 
strikes,  the  arming  resistance  must  be  less  than  the  centrifugal 
force  deve'oped  by  the  rotation  in  the  projectile  at  impact.     For 
simplicity  we  will  consider  that  the  projectile's  velocity  of  rota- 
tion at  impact  is  the  same  as  at  the  muzzle  of  the  gun. 


PRIMERS  AND  FUSES  FOR  CAXXON.  503 

Problem  4-  Determine  the  maximum  permissible  arming  re- 
sistance for  the  centrifugal  fuse  in  the  12-inch  mortar  projectile, 
for  which  we  have  the  following  data. 

Weight  of  plunger  complete,  660  grains. 

Weight  of  plunger  half,          w,  =  330  grains  -  330/7000  Ibs. 

Radius  of  center  of  gravity  of  plunger  half,  r  =  0.4  ins.  =0.4/12 ft. 

Twist  at  muzzle,  n  =  25. 

Muzzle  velocity  of  projectile,  F  =  950  f.  s. 

Diameter  of  projectile,  d  =  l2  inches  =  1  ft. 

Combining  equations  (62)  and  (61),  page  250,  we  find  for  the 
velocity  of  rotation  of  the  projectile  at  the  muzzle 

io  =  2V7z/dn  =  2  -  950/25  =  238.76 
The  centrifugal  force  acting  on  each  plunger  half  is 
F  =  mav2/f) = u\o?r2/gp 

in  which  v  is  the  linear  velocity  of  the  center  of  gravity   of  the 

plunger  half,  due  to  the  rotation, 
r  the  radius  of  the  center  of  gravity, 
ft  the  radius  of  its  path. 
At  the  beginning  of  movement  p  =  r,  and  we  have 


330X238.  762XO.  4    o 
700oX32.16Xl2  =2'79  lbs* 

for  the  force  tending  to  move  each  plunger  half. 

If  the  resistance  of  the  spring  is  less  than  2.79  lbs.  the  fuse  will 
start  to  arm. 

As  the  plunger  halves  separate,  the  resistance  of  the  spring 
increases  in  the  manner  shown  by  equation  (14),  page  285. 


It  will  be  seen,  from  the  value  of  F  above,  that  F  increases 
directly  with  r.  In  order  that  the  fuse,  after  starting  to  arm,  may 
arm  completely,  the  values  of  Gr  and  G  must  be  such,  that  is,  the 
spring  must  be  of  such  construction,  that  S  will  not  increase  more 
rapidly  than  F. 


504  ORDNANCE  AND  GUNNERY. 

287.  Problem  5.  Assume  that  the  spring  in  the  plunger  of  the 
fuse  for  the  12-inch  mortar  projectile  is  under  a  tension  of  1J  Ibs. 
What  muzzle  velocity  is  required  in  the  projectile  to  arm  the  fuse? 

We  have 


F  =  waaf2r/g 
from  which 


Solving  for  V 


The  force  required  for  arming  is  in  this  case  1.5  pounds.  Sub- 
stituting 1.5  for  F,  and  for  the  other  quantities  the  values  as  given 
in  the  preceding  problem,  we  have 

25/1.  5X32.  16X7000X12V 
'  &(  --  330X0.4         -)  =697.14  f.s. 

The  fuse  will  arm  for  any  muzzle  velocity  of  the  projectile  ex- 
ceeding 697.14  foot  seconds. 

Problem  6.  What  is  the  minimum  muzzle  velocity  that  will 
arm  the  centrifugal  fuse  described  below,  when  fired  from  a  6- 
inch  howitzer? 

Weight  of  plunger  half,  u>g  =  400  grains  =  4/70  Ibs. 

Radius  of  center  of  gravity  of  plunger  half,  r  =  0.5  in.  =0.5/12  ft- 

Spring  resistance  to  arming,  F  =  2  Ibs. 

Twist  of  rifling  at  muzzle,  n=25. 

Diameter  of  projectile,  d  =  Q  in.  =0.5  ft. 

Ans.  V  =  327  foot  seconds. 


CHAPTER  XIII. 
SIGHTS. 

288.  Purpose. — It  has  been  shown  in  exterior  ballistics  that 
in  order  that  the  projectile  from  any  gun  may  hit  the  target  the 
gun  must  be  fired  at  a  certain  angle  of  elevation,  depending  upon 
the  range  and  upon  the  relative  level  of  the  gun  and  target,  and 
must  be  given  such  direction  to  the  right  or  left  of  the  target  as 
to  neutralize  the  deviation  of  the  shot  from  the  plane  of  fire  due 
to  the  drift  and  wind. 

The  elevation  in  the  plane  of  fire  and  the  allowance  for  devia- 
tion from  the  vertical  plane  containing  gun  and  target  are  deter- 
mined beforehand  either  by  calculation  or  estimate.  Direction  is 
given  to  the  axis  of  the  gun  by  whatever  means  may  be  provided. 
The  axis  of  the  gun  when  given  the  determined  elevation  and 
deviation  has  a  fixed  relation  to  the  line  from  the  gun  to  the  target. 

The  sights  of  the  gun  provide  the  means  of  determining  when 
the  axis  of  the  gun  has  the  predetermined  direction  with  respect 
to  the  line  from  gun  to  target. 

Principle  and  Methods. — The  principle  of  sighting  is  simple. 
It  consists  in  determining,  by  means  of  the  sights,  a  line  to  which 
the  axis  of  the  gun  has  the  fixed  relation  already  determined  as 
being  required  between  the  axis  and  the  line  to  the  target;  and 
then,  by  looking  through  the  sights,  making  the  line  of  the  sights 
and  the  line  to  the  target  coincide. 

The  line  of  sight  on  a  gun  may  be  fixed  in  one  of  two  ways: 
first,  by  means  of  two  plain  or  open  sights,  the  rear  one  of  which 
has  a  peep  or  notch  capable  of  adjustment  in  vertical  and  hori- 
zontal directions;  second,  by  means  of  a  telescope,  whose  axis  or 
line  of  collimation  may  be  given  any  direction  desired. 

505 


506  ORDNANCE  AND  GUNNERY. 

In  Fig.  230  0  represents  the  peep  of  the  rear  sight  in  its  zero 
position,  the  line  from  0  to  the  front  sight  A  being  parallel  to  the 
axis  of  the  piece.  Or  the  line  OA  may  represent  the  line  of  colli- 
mation  of  a  telescope,  the  telescope  being  pivoted  at  A.  If  now 
\ve  calculate  that  to  reach  the  target  at  F,  under  the  conditions 
prevailing,  a  certain  angle  of  elevation  is  required  and  a  certain 
deviation  to  the  left,  we  lift  the  peep  of  the  rear  sight  to  the  point 
C  so  that  OAC  is  the  required  angle  of  elevation,  and  then  move 
the  peep  horizontally  from  C  to  E  to  obtain  the  required  deviation. 
The  line  of  sight  is  now  the  line  EA,  and  if  the  gun  is  maneuvered 
so  that  this  line  is  made  to  pass  through  the  target,  the  axis  has 


FIG.  230. 

then  the  elevation  and  deviation  required  under  the  existing 
conditions. 

The  gun  is  aimed  at  the  target  F,  but  its  axis,  parallel  to  the 
line  CB,  is  practically  pointed  at  B,  which  is  above  F  by  the 
vertical  distance  BD  and  to  the  left  of  F  by  the  horizontal  distance 
DF. 

TARGET  NOT  IN  VIEW. — In  the  foregoing  the  target  has  been 
assumed  to  be  in  view.  If  the  target  is  not  in  view  the  required 
position  of  the  axis  of  the  gun  with  respect  to  a  horizontal  line  in 
the  vertical  plane  through  gun  and  target  is  determined.  The 
vertical  angle  between  this  line  and  the  axis  is  the  angle  of  eleva- 
tion. This  angle  is  laid  off  by  the  sights  as  before  and  the  gun  is 
elevated  until  the  line  of  sight  AC  is  horizontal  as  determined  by 
means  of  a  spirit  level  mounted  on  the  rear  sight.  Other  means 
must  be  employed  for  determining  the  direction  in  this  case. 

289.  Graduation  of  Rear  Sights. — The  graduations  of  the 
rear  sight  for  elevation  may  be,  and  often  are,  in  degrees  and 
minutes  of  arc,  the  center  of  the  arc  being  at  the  center  of  motion 


SIGHTS,  507 

of  the  rear  sight.  But  as  the  powder  charges  of  guns  are  made 
up  to  give  certain  fixed  muzzle  velocities  to  the  projectiles,  the 
angle  of  elevation  required  to  attain  any  range  with  the  given 
muzzle  velocity  under  standard  atmospheric  conditions  may  be 
determined  in  advance,  and  the  rear  sight  be  graduated  for  range 
instead  of  angular  elevation. 

The  range  graduation  is  the  more  convenient,  for  the  range 
may  usually  be  readily  determined,  and  the  graduation  on  the 
rear  sight  indicates  at  once  the  proper  elevation. 

The  horizontal  deflection  scale,  by  means  of  which  allowance  is 
made  for  deviation  to  the  right  or  left,  is  graduated,  in  sights  for 
field  artillery,  to  thousandths  of  the  range.  These  graduations 
are  called  mils,  from  the  French  mittibmes.  It  is  apparent  from 
Pig.  230  that  if  EC  is  n  thousandths  of  AQ,  the  horizontal  dis- 
tance DF  will  be  n  thousandths  of  AD  and  practically  of  the  range 
AF.  In  sights  for  seacoast  artillery  the  least  division  of  the 
deflection  scale  is  three  minutes  of  arc,  which  corresponds  to  a 
deflection  of  0.00087  of  the  range,  approximately  1/1000. 

Correction  for  Drift. — The  deviation  of  the  projectile  due  to 
drift,  which  is  caused  by  the  rotation  of  the  projectile  and  the 
resistance  of  the  air,  may  be  determined  for  any  range  by  the 
formulas  of  exterior  ballistics,  and  thus  the  curve  of  drift  may  be 
constructed  for  any  gun.  If  then  the  rear  sight  is  so  constructed 
that  as  the  peep  is  lifted  in  elevation  to  any  range  it  is  automatic- 
ally moved  horizontally  just  enough  to  compensate  for  the  drift 
at  that  range,  the  sight  makes  automatic  correction  for  the  drift, 
and  need  be  further  adjusted  only  for  the  wind  or  other  atmos- 
pheric deviating  influences. 

In  all  service  guns  the  drift  of  the  projectile  is  to  the  right. 
The  drift  increases  with  the  range.  The  rear  sight  with  automatic 
drift  correction  therefore  moves  to  the  left  as  it  is  raised  in  eleva- 
tion. In  our  service,  automatic  drift  correction  will  be  found  only 
in  sights  for  small  arms. 

It  is  well  to  bear  in  mind  that  the  projectile  follows  the  move- 
ment of  the  rear  sight,  going  higher  as  the  sight  is  raised,  and  to 
the  right  or  left  as  the  sight  is  moved  to  the  right  or  left. 

290.  Correction  for  Inclination  of  Site. — The  angle  of  eleva- 
tion of  a  gun  is  the  angle,  in  a  vertical  plane,  that  the  axis  of  the 


508 


ORDNANCE  AND  GUNNERY. 


gun  makes  with  the  horizontal.  In  Fig.  231  let  r  be  the  point  to 
which  the  rear  sight  must  be  raised,  in  the  vertical  plane  of  the 
axis,  to  give  to  the  gun  a  desired  angle  of  elevation  equal  to  o/r,  / 
representing  the  front  sight,  h  is  a  horizontal  line  in  the  vertical 
plane  of  the  axis.  Now  suppose  the  gun  to  be  revolved  to  the 
left  about  its  axis.  The  axis  of  the  gun  remains  in  the  vertical 
plane,  but  the  points  r,  o,  and  /  revolve  to  the  left  out  of  the  plane ; 
and  as  r  is  farther  from  the  center  than  o  and  /,  its  movement  is 
greater  than  the  equal  movements  of  o  and  /.  We  may  therefore 
consider  that,  relatively  to  o  and  /,  r  takes  some  position  /.  Pro- 


FIG.  231. 


jecting  r'  on  the  Vertical  plane,  at  r",  we  see  that  the  angle  of 
sight  o//  produces  an  angle  of  elevation  o/r",  which  is  less  than  the 
desired  angle  o/r.  It  is  apparent  too  that  the  line  of  sight  through 
r7  will  cause  the  gun  to  be  pointed  to  the  left  of  the  plane  of  o/r. 

If,  however,  the  sight  is  pivoted  at  o  so  that  it  has  movement 
in  a  plane  perpendicular  to  the  axis  of  the  gun,  we  are  enabled, 
when  the  gun  has  been  revolved,  to  make  the  sight  arm  or7  ver- 
tical; and  since  the  points  o  and  /  have  revolved  together,  or', 
now  coincident  with  or,  will  subtend  the  desired  vertical  angle  o/r. 

It  is  therefore  essential  that  the  rear  sights  for  guns  that  are 
likely  to  be  fired  on  uneven  sites  shall  be  so  constructed  that  the 
sight  arm  may  revolve  about  the  zero  point  of  the  elevation  scale  in 
a  plane  perpendicular  to  the  axis  of  the  gun.  We  will  find  that 
the  rear  sights  for  all  guns  mounted  on  wheeled  carriages  are 
constructed  in  this  manner. 

Guns  of  position  are  mounted  on  carriages  that  rest  on  level 
platforms,  and  their  sights  are  so  adjusted  as  to  always  move  in  a 
vertical  plane. 


SIGHTS.  509 

Location  of  Sights. — Sights  for  all  guns  are  now  placed  on 
some  non-recoiling  part  of  the  gun  carriage,  and  the  elevating  and 
traversing  mechanisms  are  under  the  control  of  the  cannoneer  at 
the  sights,  so  that  the  operation  of  sighting  may  go  on  continuously 
during  the  loading  arid  firing  of  the  piece. 

LIXE  SIGHTS. — Most  guns  are  provided  with  line  sights  fixed 
to  the  gun.  They  serve  only  to  give  general  direction  to  the  piece, 
and  consist  of  a  front  stud  with  conical  point,  and  a  notched  bar 
on  the  top  of  the  breech.  The  line  extending  from  a  point  over 
the  center  of  the  notch  at  the  level  of  the  top  of  the  bar  to  the 
point  of  the  front  sight  is  parallel  to  the  axis  of  the  piece. 

The  most  recent  service  sights  and  other  appliances  used  in 
gun  pointing  will  now  be  described.  The  sights  mounted  on  the 
various  guns  of  older  model  will  readily  be  understood  after  a 
study  of  these. 

291.  Sights  for  Mobile  Artillery. — The  appliances  provided 
for  sighting  the  3-inch  field  piece,  and  other  pieces  on  wheeled 
carriages,  include  line  sights,  the  adjustable  or  tangent  sight,  the 
panoramic  sight  and  the  range  quadrant. 

The  line  sights  are  fixed  to  the  gun  as  already  de- 
scribed. 

The  Adjustable  or  Tangent  Sight. — The  adjustable  sight  con- 
sists of  a  fixed  front  sight  and  an  adjustable  rear  sight. 

The  front  sight,  supported  in  a  bracket  on  the  cradle,  is  a  short 
tube,  Fig.  232,  whose  axis  is  marked  by  the  intersection  of  two 
cross  wires  set  in  the  tube  at   angles   of 
45  degrees  with  the  horizon.     A  bead  on 
top  of  the  tube  serves  for  approximate 
determination  of  direction. 

The  rear  sight,  Fig.  233,  is  shown 
viewed  from  the  left  in  the  left-hand 
figure,  and  from  the  rear  in  the  figure  on 
the  right.  The  rear  sight  bracket  is  seated  FIG.  232. 

in  a  socket  attached  to  the  cradle  of  the 

carriage,  on  the  left  side.  At  the  upper  end  of  the  bracket  two 
seats  are  formed  for  the  attachment  of  the  socket  for  the  sight. 
The  seats  are  faced  in  a  plane  perpendicular  to  the  axis  of  the 


510 


ORDNANCE  AND  GUNNERY. 


piece  and  circular  guides  are  cut  on  them,  with  the  zero  index  of 
the  elevation  scale  as  a  center. 

The  shank  socket  which  holds  the  rear  sight  is  mounted  on  the 
bracket  and  has  circular  motion  on  the  guides  under  the  action  of 


the  transverse  leveling  screw.  This  arrangement  permits  the 
correction  for  inclination  of  site  by  revolution  of  the  rear  site  in  a 
pkne  perpendicular  to  the  axis  of  the  gun  until  the  sight  is  ver- 
tical, as  indicated  by  the  transverse  level  fixed  to  the  socket. 


SIGHTS.  511 

The  sight  shank  is  an  arm  curved  to  the  arc  of  a  circle  whose 
center  is  the  front  sight.  The  shank  slides  up  and  down  in  guides 
in  the  socket,  its  movement  being  effected  by  the  thumb  nut, 
called  the  elevating  gear  hand  wheel,  through  a  scroll  gear  wheel 
which  acts  on  the  teeth  of  the  rack  cut  on  the  right  face  of  the 
shank.  The  scroll  gear  is  held  in  mesh  by  a  spring.  By  pulling 
out  the  thumb  nut  the  gear  is  disengaged  from  the  rack,  and  a 
large  change  in  elevation  may  then  be  rapidly  made  by  sliding  the 
shank  through  the  socket  by  hand. 

The  range  scale  is  marked  on  the  rear  face  of  the  shank,  and  is 
read  at  the  index  at  the  upper  end  of  the  socket.  The  smallest 
division  of  the  scale  corresponds  to  50  yards  of  range,  but  this  may 
be  readily  subdivided  by  the  eye. 

On  the  upper  end  of  the  shank  is  a  frame  in  which  is  mounted 
the  peep  of  the  rear  sight.  The  peep  is  moved  to  the  right  or  left 
by  means  of  the  deflection  screw7.  The  peep  hole  is  1/10  of  an 
inch  in  diameter.  The  divisions  of  the  deflection  scale  correspond 
to  one  mil,  I/ 1000  of  the  range.  The  scale  is  marked  from  left  to 
right  as  follows : 

40        30        20        10        0        90        80        70        6360 

The  deflection  readings  arc  uniform  with  those  of  the  pano- 
ramic sight  and  battery  commander's  telescope.  They  will  be 
explained  later  in  the  description  of  the  panoramic  sight. 

The  sight  is  continued  upward  above  the  seat  for  the  peep  to 
form  a  seat  for  the  panoramic  sight. 

The  axis  of  the  clinometer  level  is  parallel  to  the  line  of  sight, 
and  thus  permits  the  use  of  the  sight  as  a  quadrant  in  giving  ele- 
vation to  the  piece  when  the  target  is  not  in  view. 

In  the  sight  for  the  6-inch  how-itzer,  see  Fig.  132,  the  front 
sight  is  mounted  on  the  same  bar  as  the  rear  sight,  and  the  bar 
revolves  in  elevation  about  a  point  between  the  twro  sights.  The 
rear  sight  has  a  sliding  movement  in  deflection  on  the  end  of  the  bar. 

The  adjustable  sight  is  often  called  a  tangent  sight  from  its 
similarity  to  the  sights  with  straight  shanks  formerly  much  used 
with  cannon.  The  peep  of  the  tangent  sight  moves  on  the  tan- 
gent of  an  arc  instead  of  on  the  arc  itself.  The  rear  sight  for  the 
30-caliber  rifle  is  a  tangent  sight. 


512  ORDNANCE  AND  GUNNERY. 

For  field  howitzers  the  seats  for  the  front  and  rear  sights  are 
alike,  so  that  the  positions  of  the  sights  may  be  reversed  for  in- 
direct sighting,  which  consists  in  directing  the  line  of  sight  at  any 
object  other  than  the  target. 

292.  The  Panoramic  Sight. — The  fire  from  modern  field  guns 
is  so  accurate  and  destructive  that  it  has  been  found  necessary  in 
recent  battles  to  establish  field  batteries  always  in  positions  out 
of  view  of  the  enemy,  in  order  to  protect  the  batteries  from  the 
fire  of  the  enemy's  guns. 

Indirect  sighting  becomes  then  of  necessity  the  usual  method 
of  sighting  guns  in  battle. 

The  panoramic  sight  affords  the  means  of  aiming  the  gun  by 
directing  the  line  of  sight  on  any  object  in  view  from  the  gun. 
At  the  same  time  it  offers  the  advantages  of  a  telescopic  sight  in 
direct  or  indirect  aiming. 

The  panoramic  sight  is  a  telescope  so  fitted  with  reflectors  and 
prisms  that  a  magnified  image  of  an  object  anywhere  in  view 
may  be  brought  to  the  eye  without  change  in  the  direction  of 
sight. 

The  panoramic  sight  for  the  field  and  siege  guns  is  shown  in 
Fig.  234.  The  rays  of  light  from  the  object  viewed  enter  the 
sight  through  the  plain  glass  window-  in  the  head  piece  and  are 
bent  downward  by  the  prism  of  total  reflection  A,  rectified  ver- 
tically by  the  prism  B,  focussed  by  the  object  lens  C,  and  rectified 
laterally  by  the  gabled  prism  D,  so  that  there  is  presented  to  the 
eyepiece  E  a  rectified  image  of  the  object,  which  image  is  magni- 
fied by  the  two  lenses  of  the  eyepiece. 

The  magnifying  power  of  the  instrument  is  4  and  the  field  of 
view  is  10  degrees. 

THE  ROTATING  PRISM. — The  interior  tube  containing  the  prism 
B  and  the  objective  C  is  mounted  so  that  it  may  rotate  in  the 
body  of  the  telescope. 

The  prism  B  is  rectangular  in  cross  section.  Its  upper  and 
lower  faces  are  oblique  to  its  axis,  and  its  length  is  such  that  a  ray 
that  enters  the  prism  axially  emerges  axially.  Even-  ray  entering 
parallel  to  the  axis  therefore  emerges  at  an  equal  distance  on  the 
other  side  of  the  axis.  A  vertical  ray  entering  the  prism  at  a,  Fig. 
235,  is  reflected  by  the  back  of  the  prism  and  emerges  at  c.  Now 


SIGHTS. 


513 


FIG.  235. 


if  the  prism  is  revolved  through  any  angle,  say  4$  degrees,  as  repre- 
sented in  the  figure  by  the  position  shown  in  broken  lines,  the  ray 
a  will  emerge  at  e,  the  back  of  the  prism  now  being  at  the  angle 
of  45  degrees  with  its  original  position;  and  the  X/NX 

angle  through  which  the  ray  has  moved,  measured 
from  the  axis  of  the  prism,  which  is  the  axis  of 
rotation,  is  90  degrees.  The  angular  movement  of 
the  ray  is  therefore  double  the  angular  movement 
of  the  prism.  Consequently  the  image  of  an  object 
seen  through  the  prism  rotates  through  twice  the 
angle  of  rotation  of  the  prism. 

The  head  piece  containing  the  prism  A  is  also 
mounted  to  rotate  on  the  body  of  the  telescope, 
and  in  order  to  counteract  the  doubled  angular 
movement  of  the  image  by  the  prism  B,  the  head 
piece  is  made  to  rotate  twice  as  fast  as  the  prism. 
The  image  of  any  object  then  rotates  through  the 
same  angle  as  the  head  piece,  and  the  relative  positions  of  objects 
in  the  field  of  view  are  not  changed. 

The  different  movements  of  A  and  B  are  accomplished  by 
means  of  one  tangent  screw  through  gearing  contained  in  the 
cylindrical  casing  seen  at  the  junction  of  the  rotating  parts. 

THE  GRADUATED  SCALE. — The  angular  movement  of  the  head 
piece  is  indicated  by  a  graduated  scale  on  its  perimeter,  visible 
through  a  window  in  the  rear  of  the  casing.  When  the  index  on 
the  casing  is  at  the  zero  of  the  scale,  the  line  of  sight  of  the  pano- 
ramic sight  is  in  the  vertical  plane  parallel  to  the  axis  of  the  piece. 
If  at  the  same  time  the  tangent  sight  on  which  the  panoramic  sight 
is  mounted  is  at  the  zero  of  the  elevation  scale,  the  line  of  sight  of 
the  panoramic  sight  is  parallel  to  the  axis  of  the  piece. 

In  the  scale  on  the  head  piece  the  circle  is  divided  in  64  equal 
parts,  numbered  clockwise.  One  complete  turn  of  the  tangent 
screw  moves  the  head  piece  through  one  of  these  angles.  A 
micrometer  scale  mounted  on  the  shaft  of  the  tangent  screw  has 
100  equal  divisions.  .A  movement  of  the  tangent  screw  through 
one  of  the  divisions  of  the  micrometer  scale  therefore  moves  the 
head  piece  through  1/6400  of  a  circle;  which  angle  corresponds 
very  closely  to  1/1000  of  the  range.  The  reading  of  the  scales  is 


514  ORDNANCE  AND  GUNNERY. 

in  6400ths  of  the  circle.  The  hundreds  are  read  from  the  scale 
on  the  head  piece,  and  tens  and  units  from  the  scale  on  the  tangent 
screw.  Thus  if  the  index  has  passed  the  mark  27  on  the  head 
scale,  and  the  index  of  the  micrometer  scale  stands  at  18,  the 
reading  is  2718. 

Referring  now  to  the  readings  on  the  deflection  scale  of  the 
tangent  sight,  page  511,  we  see  that  the  first  reading  to  the  left 
of  the  zero,  which  is  10,  indicates  a  position  of  the  tangent  sight 
parallel  to  the  position  of  the  panoramic  sight  when  the  index  of 
the  scale  on  the  head  of  the  panoramic  sight  is  between  0  and  1 
of  the  scale,  and  the  index  of  the  micrometer  scale  is  at  10.  Simi- 
larly the  reading  90,  to  the  right  of  the  zero,  indicates  the  position 
of  the  panoramic  sight  between  63  and  64  of  the  head  scale  with 
the  micrometer  scale  at  90.  The  reading  of  the  panoramic  sight 
is  then  6390. 

USE  AS  A  RANGE  FINDER. — As  horizontal  angles  may  be 
measured  with  the  panoramic  sight  the  sight  may  be  used  as  a 
range  finder.  Using  the  line  between  the  sights  of  the  flank  guns 
of  a  battery  as  a  base  the  triangle  formed  by  the  two  sights  an  1 
the  target  may  be  determined. 

ON  SEACOAST  CARRIAGES. — Trials  are  now  being  made  of  the 
panoramic  sight  applied  to  disappearing  carriages.  The  sight  is 
attached  to  the  left  cheek  of  the  chassis  with  the  eye  end  of  the 
sight  at  a  height  convenient  for  the  gunner  standing  on  the  racer 
platform.  The  vertical  tube  of  the  sight  is  of  length  sufficient  to 
bring  the  head  of  the  sight  above  the  crest  of  the  parapet. 

293.  The  Range  Quadrant. — In  rapid  firing,  the  duties  of 
setting  the  sight  for  range  and  deflection,  and  laying  the  piece  by 
manipulating  the  elevating  and  traversing  mechanisms  would,  if 
attended  to  by  a  single  cannoneer,  frequently  delay  the  firing 
much  beyond  the  time  required  to  load.  Since  in  the  carriages  for 
mobile  artillery  the  elevating  and  traversing  mechanisms  are 
entirely  independent  of  each  other,  the  pointing  of  the  piece  may 
be  much  simplified  and  the  time  required  be  considerably  lessened 
by  assigning  to  one  cannoneer  the  pointing  of  the  piece  for  direc- 
tion and  to  a  second  the  elevation  of  the  piece  for  range.  Such  a 
division  of  duties  is  provided  for  by  the  elevating  crank  at  the 
right  side  of  the  trail  and  by  the  range  quadrant  attached  to  the 


SIGHTS. 


515 


right  of  the  cradle.     By  this  arrangement,  the  gunner  on  the  left 
of  the  piece,  using  the  open  or  panoramic  sight,  lays  for  direction 


a 

•+J 

a 

2 

•s 

(§> 


only,  while  the  cannoneer  on  the  right  of  the  piece  gives  quadrant 
elevations. 

The  range  quadrant,  Fig.  236,  is  supported  in  a  bracket  on  the 
right  side  of  the  cradle  of  the  carriage  with  its  axis  parallel  to  the 
vertical  plane  containing  the  axis  of  the  piece;  and  provision  is 


516  ORDNANCE  AND  GUNNERY. 

made  for  rotation  of  the  quadrant  about  its  axis  in  order  that  the 
curved  rocker  arm  of  the  quadrant  may  be  made  vertical  when  the 
wheels  of  the  carriage  are  on  different  levels.  The  vertical  posi- 
tion of  the  quadrant  arm  is  indicated  by  the  transverse  level. 

The  quadrant  consists  of  a  fixed  arm  of  which  the  rocker  arm 
is  a  part:  and  a  movable  arm,  in  front  of  the  fixed  arm  in  the 
figure,  carrying  a  range  disk,  a  clinometer  level,  and  the  mechanism 
for  elevating  the  movable  ami.  The  fixed  arm  has  at  the  rear  an 
upwardly  extending  arc,  called  the  rocker  arm,  with  toothed 
racks  on  front  and  rear  edges.  The  movable  arm,  pivoted  at  the 
front  to  the  fixed  arm,  is  given  motion  about  its  pivot  by  a  gear 
actuated  by  the  elevating  hand  wheel  and  meshing  in  the  rearmost 
rack.  A  pinion  on  the  shaft  of  the  range  disk  meshes  in  the  for- 
ward rack,  and  the  movement  of  the  arm  in  elevation  is  indicated 
by  the  scale  on  the  range  disk  in  terms  of  the  corresponding 
range. 

THE  CLINOMETER. — The  clinometer  level  is  pivoted  on  the  axis 
of  the  movable  arm,  and  may  be  moved  relatively  to  the  arm  by 
the  clinometer  level  screwy  the  upper  end  of  which  carries  a  microm- 
eter scale.  A  short  circular  scale  is  marked  on  the  left  edge  of  the 
piece  carrying  the  level.  The  level  scale  is  in  64ths  of  a  circle,  and 
the  micrometer  scale  in  6400ths,  similar  to  the  scales  of  the  pano- 
ramic sight. 

The  purpose  of  the  clinometer  is  to  make  correction  for  differ- 
ence in  level  of  the  gun  and  target.  The  angle  subtended  at  the 
target  by  the  difference  in  level  is  called  the  angle  of  site,  as  may 
be  seen  by  the  words  on  the  clinometer  level  in  the  figure.  In 
exterior  ballistics  we  have  called  this  angle  the  angle  of  position, 
which  is  a  better  term,  first  in  better  expressing  wrhat  is  meant, 
and  second  in  not  leading  to  confusion  through  similarity  to  the 
word  sight,  and  to  the  term  angle  of  sight,  in  frequent  use. 

The  readings  on  the  clinometer  scale  are  2,  3,  and  4,  read  200, 
300,  and  400,  to  which  are  added  the  readings  of  the  micrometer 
scale.  300  corresponds  to  the  horizontal  position  of  the  axis  of 
the  gun.  The  angle  of  position,  expressed  in  6400ths  of  the  circle, 
is  obtained  by  subtracting  the  reading  of  the  scales  from  300.  If 
the  reading  is  greater  than  300  the  result  is  negative  and  the  target 
is  belowr  the  gun. 


SIGHTS.  517 

294.  USE  OF  THE  QUADRANT. — The  quadrant  is  used  as  follows. 
The  gun  is  pointed  at  the  target  by  means  of  the  line  sights,  the 
quadrant  being  set  at  the  zero  of  the  range  scale.     The  quadrant 
is    leveled    transversely,  and  the   clinometer  level   is  leveled  by 
means  of  its  screw.    The  angle  indicated  on  the  clinometer  scale  is 
the  angle  of  position  of  the  target.     Further  movement  of  the  gun 
in  elevation  is,  by  means  of  the  clinometer,  measured  from  this 
position  of  the  gun  as  zero.     The  movable  arm  of  the  quadrant  is 
elevated  until  the  range  of  the  target  is  recorded  on  the  range 
scale.     The  piece  is    then  elevated  until  the  clinometer  level    is 
again  level.    The  piece  has  now  the  proper  angle  of  elevation  for 
the  range  increased  or  diminished  by  the  angle  of  position,  accord- 
ing as  the  target  is  higher  or  lower  than  the  gun. 

It  will  be  noted  that  in  the  use  of  the  clinometer  in  correcting 
the  angle  of  elevation  by  adding  or  subtracting  the  angle  of  posi- 
tion we  are  applying  the  principle  of  the  rigidity  of  the  trajectory. 

The  Battery  Commander's  Telescope  and  Ruler. — The  bat- 
tery commander's  telescope  and  the  battery  commander's  ruler, 
used  as  aids  in  determining  the  elements  of  sighting  for  pieces 
employed  in  indirect  fire,  should  perhaps  be  classed  as  range  and 
position  finders  rather  than  as  appliances  for  sighting.  They  will 
be  described  in  the  chapter  on  range  and  position  finding,  which 
follows  this  chapter. 

Telescopic  Sights. — The  advantages  gained  by  the  use  of  a 
telescope  in  laying  a  piece  consist  in  an  increased  power  of  vision 
and  a  large  decrease  in  personal  error.  The  telescope  renders  dis- 
tinct an  object  that  may  be  barely  visible  to  the  naked  eye  and 
enables  the  gunner  to  lay  the  gun  on  such  an  object  with  accuracy 
and  facility. 

Telescopic  sights  are  now  used  on  all  guns  of  position.  They 
are  fixed  to  the  non-recoiling  cradle  of  the  barbette  mount,  and 
to  the  chassis  of  the  disappearing  mount.  Hand  wheels,  or  electric 
controllers,  for  the  manipulation  of  the  mechanisms  for  laying  the 
piece  are  in  positions  convenient  to  the  gunner  at  the  sight,  and  in 
addition  an  electric  firing  pistol  is  placed  at  his  hand  so  that  all  the 
operations  of  aiming  and  firing  the  piece  are  under  his  control. 

295.  Telescopic  Sight,  Model  1904. — The  latest  pattern  of 
telescopic  sight,  model  1904,  for  guns  mounted  on  disappearing 


518  ORDNANCE  AND  GUNNERY. 

carriages,  is  shown  in  Fig.  237;  see  also  Fig.  145.  Sights  of  the 
same  model  are  provided  also  for  barbette  carriages.  They  differ 
from  the  sight  described  only  in  the  method  of  attachment  to  the 
carriage. 

The  sight  arm  a  is  pivoted  at  its  forward  end  on  the  sight 
standard  of  the  carriage  arid  is  supported,  by  a  pin  through  the 
hole  near  its  rear  end,  on  a  vertical  rod  so  connected  with  the 
elevating  mechanism  of  the  gun  that  it  gives  to  the  sight  arm  the 
same  movement  in  elevation  that  is  given  to  the  gun,  see  Figs. 
145  and  146.  A  curved  guide  g,  moving  in  a  groove  in  the  stand- 
ard, keeps  the  sight  arm  in  the  vertical  plane.  A  cradle  c  carry- 
ing the  telescope  t  is  pivoted  to  the  forward  end  of  the  sight  arm 
in  such  a  manner  that  the  cradle  has  both  vertical  and  horizontal 
movement  about  its  pivot.  Vertical  movement  is  given  by  the 
hand  wheel  e  which  actuates  a  gear  mounted  on  the  sight  arm 
and  meshing  in  the  rack  on  the  shank  s.  The  cradle  is  given 
horizontal  movement  on  the  head  of  the  shank  by  the  deflection 
screw  d.  On  the  rear  face  of  the  shank  is  an  elevation  scale 
graduated  to  degrees  and  minutes  of  arc,  the  least  reading  being 
6  minutes.  A  deflection  scale  on  the  rear  end  of  the  cradle  under 
the  telescope  extends  over  4  degrees  of  arc.  The  degree  marks  are 
numbered  from  1  on  the  right  to  5  on  the  left,  the  3-degree  mark 
corresponding  to  no  deflection.  The  least  reading  of  the  deflection 
scale  is  3  minutes,  which  corresponds  approximately  to  a  deflec- 
tion of  one  mil. 

When  the  sight  is  set  at  the  zero  of  the  elevation  and  deflection 
scales  the  axis  of  the  telescope  is  parallel  to  the  axis  of  the  piece. 

A  range  drum  ra  connected  with  the  elevating  gear  of  the  sight 
indicates  the  range  corresponding  to  any  position  of  the  sight. 
The  range  drum  contains  a  coiled  ribbon  spring  arranged  to  equal- 
ize the  efforts  in  elevating  and  depressing  the  sight. 

A  peep  sight  p  is  mounted  above  the  eye  end  of  the  telescope, 
and  an  open  front  sight  /,  with  crossed  wires,  is  mounted  above  the 
forward  end  of  the  cradle. 

Electric  lamps  /  illuminate,  in  night  sighting,  the  elevation 
and  deflection  scales  and  the  cross  hairs  in  the  telescope. 

THE  TELESCOPE.— The  construction  of  the  telescope  will  be 
understood  from  Fig.  238.  The  achromatic  object  glass  o,  com- 


SIGHTS. 


519 


posed  of  three  lenses,  has  a  clear  aperture  3  inches  in  diameter 
and  a  focal  length  of  17.25  inches.  The  length  of  the  telescope  is 
diminished  and  an  erect  image  presented  to  the  eyepiece  by  means 
of  the  two  Porro  prisms  p.  In  the  figure  the  prisms  appear  to  be 
so  placed  that  each  intercepts  a  ray  of  light  entering  or  issuing 
from  the  other,  but  in  reality  the  prisms  are  offset  from  each  other 
so  that  the  light  has  unobstructed  passage  to  and  from  them. 
One  prism  is  horizontal  and  the  other  stands  vertically.  The 
lower  prism  by  its  inclined  surfaces  bends  the  ray  twice  through 
angles  of  90  degrees,  reflecting  it  back  to  the  upper  prism,  which 
again  bends  it  twice  and  reflects  it  into  the  field  of  the  eyepiece. 
The  image,  rectified  horizontally  and  vertically  by  the  prisms,  is 


LT 


FIG.  238. 


focussed  in  a  plane  marked  by  horizontal  and  vertical  cross  wires 
r  carried  in  a  ring,  and  is  magnified  by  the  two  lenses  of  the  eye- 
piece. The  ring  carrying  the  cross  wires  is  mounted  in  a  tube  d 
called  the  draw  tube  which  may  be  given  movement  in  and  out 
by  rotation  of  the  focussing  ring  /.  The  eyepiece  has  a  screw 
motion  out  and  in. 

Two  different  eyepieces  are  provided  with  the  telescope,  their 
magnifying  powers  being  12  and  20  diameters  respectively.  The 
field  of  view 'of  the  telescope  with  the  12-power  eyepiece  is  3.6 
degrees,  and  with  the  20-power  eyepiece  2.6  degrees. 

In  the  use  of  the  instrument  the  eyepiece  is  first  adjusted  until 
the  cross  wires  are  distinctly  defined.  The  cross  wires  are  then 
brought  into  the  focal  plane  of  the  objective  by  turning  the  focus- 
sing ring  until  the  object  viewed  is  also  distinctly  defined  and 
does  not  appear  to  move  when  the  eye  is  shifted  from  side  to  side. 
An  objective  once  focussed  is  correct  for  all  observers,  but  the 
eyepiece  requires  focussing  for  each  individual. 

Small  electric  lamps  of  about  2  candle  power,  /  Fig.  237,  illu- 


520 


ORDNANCE   AND  GUNNERY. 


minate,  in  night  sighting,  the  cross  wires  at  r  and  the  elevation 
and  deflection  scales  in  the  vicinity  of  the  indexes.  The  lamp 
that  illuminates  the  cross  wires  is  attached  outside  the  draw  tube 
and  its  light  is  reflected  by  two  mirrors  through  two  slits  cut 
through  the  tube  at  right  angles  to  each  other.  The  light  from 
each  mirror  is  thrown  upon  the  full  length  of  a  cross  wire,  and  the 
wires  appear  as  bright  lines  in  a  dark  field. 

296.  Telescopic  Sight,  Model  185  3.— The  telescopic  sight, 
model  1898,  illustrated  in  Fig.  240,  is  provided  for  the  8-,  10-,  and 
12-inch  barbette  carriages  and  for  disappearing  carriages  of  the 
earlier  models.  A  seat  for  the  sight  is  attached  to  the  chassis. 
When  mounted  in  this  seat  the  sight  is  used  to  give  to  the  gun 
direction  in  azimuth  only. 

A  seat  is  also  provided  on  the  trunnion  of  the  gun,  and  in  this 
seat  the  sight  may  be  used  in  giving  both  elevation  and  direction. 
The  bracket  &,  Fig.  240,  is  screwed  to  the  trunnion.  The  tele- 
scope is  mounted  in  a  frame  whose  trunnions  t  rest  in  notches  in 
the  bracket.  The  frame  and  telescope  are  leveled  transversely  by 
the  screw  /  which  bears  against  a  lug  projecting  from  the  trun- 
nion shaft  of  the  frame. 

ERECTING  PRISMS. — To  rectify  the  image  of  the  object  there  is 
mounted  in  the  telescope  between  the  objective  and  the  eyepiece 
a  Hastings-Brashear  compound  erecting  prism,  Fig.  239.  The 


FIG.  239. 


compound  prism  is  composed  of  two  prisms,  a,  whose  angles  are 
30,  60,  and  90  degrees,  laid  with  their  30-degree  angles  toward 
each  other  on  a  parallel-sided  glass  plate  6.  On  the  other  side  of 
the  plate  is  fixed  a  gabled  prism  c  with  a  90-degree  angle.  The 
upper  prisms  rectify  the  image  vertically,  and  the  lower  prism 


SIGHTS.  521 

horizontally,  as  may  be  seen  by  following  the  course  of  the  ray  of 
light  shown  in  the  figure. 

The  telescope  is  pivoted  at  its  forward  end  to  the  frame  and  is 
given  movement  in  elevation  by  the  screw  e,  Fig.  240.  The  ele- 
vation scale  is  read  to  one  minute  by  a  micrometer  scale  under 
the  screw  head. 

Deflection  is  given  by  moving  the  vertical  cross  wire  in  the 
telescope  to  the  right  or  left  by  means  of  the  deflection  screw  d, 
and  then  moving  the  gun  until  the  intersection  of  the  vertical  and 
horizontal  cross  wires  covers  the  point  aimed  at. 

There  are  two  deflection  scales,  one  inside  the  telescope  and 
one  outside.  The  inside  scale,  of  horn,  is  in  the  focal  plane  of  the 
telescope  and  is  seen  at  the  same  time  with  the  object  viewed. 
The  scale  is  graduated  in  divisions  of  3  minutes,  and  the  degrees 
are  numbered  from  1  on  the  right  to  5  on  the  left  as  in  the  model 
1904  telescopic  sight.  The  cross  wires  in  the  telescope  appear  in 
front  of  the  scale.  The  vertical  cross  wire  is  attached  to  a  sliding 
diaphragm  which  is  actuated  by  the  deflection  screw  d  and 
moves  the  vertical  wire  to  any  desired  degree  of  deflection  to  the 
right  or  left. 

In  sighting,  the  intersection  of  the  cross  wires  is  brought  in  line 
with  the  object  sighted. 

The  outside  deflection  scale,  s  Fig.  240,  corresponds  in  move- 
ment with  the  scale  inside  the  telescope.  Both  scales  are  read  to 
minutes  by  the  graduations  on  the  micrometer  head  d. 

In  a  telescopic  sight  the  cross  wires  inside  the  telescope  form 
virtually  the  front  sight,  and  the  aperture  of  the  eyepiece  forms 
the  rear  sight.  With  the  telescope  just  describedd  eflection  is 
given  by  moving  the  vertical  cross  wire  to  the  right  or  left,  and 
this  movement  is  equivalent  to  moving  the  front  sight  to  the 
right  or  left.  We  have  seen  on  page  507  that  with  the  front 
sight  fixed  the  projectile  follows  the  movement  of  the  rear  sight. 
When  the  rear  sight  is  fixed  a  movement  of  the  front  sight  is 
equivalent  to  a  movement  of  the  rear  sight  in  the  opposite  direc- 
tion. Therefore  with  the  telescopic  sight,  model  1898,  the  pro- 
jectile will  be  moved  to  the  right  by  movement  of  the  vertical 
cross  wire  to  the  left,  and  to  the  left  by  movement  of  the  vertical 
wire  to  the  right. 


522  ORDNANCE  AND  GUNNERY. 

297.  The  Power  and  Field  of  View  of  Telescopes. — The  power 
of  a  telescope,  the  ratio  of  the  apparent  angle  subtended  by  any 
object  to  the  actual  angle  which  the  object  subtends,  may  be  ob- 
tained by  dividing  the  aperture  of  the  object  lens  by  the  aperture 
of  the  eye  lens.    The  telescope  of  the  model  1904  sight  has  an 
objective  with  an  aperture  of  3  inches.     The  eye  lens  of  one  of  the 
eyepieces  provided   has  an  aperture  of  J  of  an  inch.     The  power 
of  the  telescope  with  this  eyepiece  is  therefore  12.     In  the  telescope 
of  the  model  1898  sight  the  aperture  of  the  objective  is  1J  inches 
and  of  the  eye  lens  £  of  an  inch.    The  telescope  has  therefore 
approximately  a  power  of  8. 

The  eye  receives  the  maximum  amount  of  light  through  a  tele- 
scope when  the  diameter  of  the  pencil  of  light  emerging  from  the 
eyepiece  is  equal  to  the  diameter  of  the  pupil  of  the  eye.  In  the 
normal  eye  the  diameter  of  the  pupil  varies  approximately  from 
\  of  an  inch  to  \  of  an  inch,  according  as  there  is  much  light  or 
little. 

The  field  of  view  of  a  telescope  is  equal  to  the  field  of  the  eye- 
piece divided  by  the  power  of  the  telescope.  The  telescope  of  the 
model '1898  sight  has  a  power  of  8  and  its  eyepiece  has  a  field  of 
48  degrees.  The  field  of  view  of  the  telescope  is  therefore  6  de- 
grees. 

The  field  of  view  of  the  same  telescope  with  different  eyepieces 
varies  practically  in  inverse  ratio  to  the  power  of  the  telescope. 

298.  Aiming  Mortars. — Mortars,  both  field  and  seacoast,  are 
as  a  rule  located  out  of  view  of  their  targets  and  usually  behind 
high  shelter.     Seacoast  mortars  are  permanently  emplaced.   Their 
carriages  are  provided  with  graduated  azimuth  circles  by  means  of 
which  the  piece  may  be  laid  at  any  given  angle  with  the  meridian 
plane.    The  angle  made  with  the  meridian  plane  by  the  line  to 
the  target  is  determined  by  means  of  range  and  position  finders. 
The  piece  is  then  laid  at  that  angle  by  means  of  the  graduations 
on  the  azimuth  circle,  and  correction  is  made  for  drift  and  devia- 
tion due  to  the  wind. 

For  giving  direction  to  field  and  siege  mortars  the  vertical  plane 
through  gun  and  target  is  established  by  stakes,  or  by  trestles  with 
plumb  lines,  set  up  either  in  front  of  or  behind  the  mortar  in  such  a 
position  that  both  gun  and  target  are  in  view.  The  axis  of  the 


SIGHTS. 


523 


mortar  is  brought  into  this  plane  or  into  any  determined  position 
with  respect  to  the  plane,  and  the  first  round  is  fired.  Correction 
for  error  in  direction  is  afterwards  made  by  means  of  marks  on 
the  platform. 

The  Gunner's  Quadrant. — Elevation  is  given  to  mortars  by 
means  of  the  gunner's  quadrant  shown  in  Fig.  241.    The  movable 


^ 

"x^ 

Line.  of  Fire-Depression..^ 

-^-^~ 

r                                                                             ^ 

FIG.  241. 

arm  6  carries  a  spirit  level  and  may  be  set  at  any  desired  angle 
with  the  base  of  the  instrument  up  to  65  degrees.  The  notched 
scale  fixes  positions  for  the  arm  6  at  whole 
degrees.  Minutes  are  obtained  by  sliding 
the  level  along  the  scale  on  the  curved  ami 
6.  The  principle  of  the  sliding  level  on  the 
curved  arm  will  be  readily  understood  by 
reference  to  Fig.  242. 

The  quadrant  may  be  used  to  measure 
angles  of  elevation  or  of  depression  from  0 
to  65  degrees. 

The  quadrant,  set  to  any  desired  angle  of  elevation,  is  placed 
on  the  gun  on  a  seat  prepared  for  it  parallel  to  the  axis  of  the 
piece.  The  instrument  is  so  placed  that  the  proper  arrow  on  its 


FIG.  242. 


524  ORDNANCE  AND   GUNNERY. 

base  points  in  the  direction  of  the  line  of  fire.  The  piece  is  then 
elevated  until  the  bubble  of  the  level  is  in  the  middle  of  the  tube. 

By  placing  the  instrument  on  a  vertical  seat,  as  for  instance 
the  face  of  the  breech  or  muzzle  of  a  gun,  angles  greater  than  25 
degrees  from  the  vertical  may  be  measured.  The  angle  is  ob- 
tained by  subtracting  the  reading  of  the  quadrant  from  90  degrees. 

To  facilitate  the  elevating  of  the  mortar  the  quadrant  is  now, 
on  mortars  mounted  on  the  model  1896  carriage,  permanently 
fixed  to  a  seat  provided  on  the  right  rimbase  of  the  mortar.  The 
level  is  fixed  on  the  movable  arm  of  the  quadrant,  and  minutes  of 
elevation  are  obtained  through  movement  of  the  arm  by  means  of 
a  tangent  screw  at  its  end. 


CHAPTER  XIV. 
RANGE  AND  POSITION  FINDING. 

299.  Definitions. — A  range  finder  is  an  instrument  for  deter- 
mining the  range  from  the  observer  to  any  distant  object. 

A  position  finder  is  an  instrument  for  determining  the  position 
of  an  object  with  respect  to  any  plane  or  line,  as  the  meridian  plane 
for  guns  of  position  or  the  front  of  a  battery  for  mobile  artillery. 

An  instrument  adapted  to  perform  both  functions  becomes  a 
range  and  position  finder. 

Range  Finders. — With  all  practical  range  finders  the  deter- 
mination of  the  range  comes  from  the  solution  of  a  triangle.  The 
target  is  the  apex  of  the  triangle.  The  base  of  the  triangle  is  laid 
off  either  vertically  or  horizontally  from  the  instrument,  and  the 
angles  at  the  extremities  of  the  base  are  determined,  one  or  both 
of  them,  by  means  of  the  instrument. 

In  determining  any  fixed  range  the  effect  of  an  error  in  the 
measurement  of  an  angle  at  the  base  of  the  triangle  will  diminish 
as  the  length  of  the  base  increases.  This  is 
apparent  from  Fig.  243.  A  given  range  ot 
is  less  affected  by  an  angular  error  the 
made  at  the  end  of  the  base  ob  than  by  an 
equal  error  tac  made  at  the  end  of  the 
shorter  base  oa.  FJG  243. 

It  is  therefore  always  desirable  to  use  as 

long  a  base  as  can  be  conveniently  obtained.  For  this  reason 
horizontal  base  lines  are  preferred,  since  the  vertical  base  of  any 
range  finder  is  limited  in  length  to  the  height  of  the  instrument 
above  the  water. 

525 


526  ORDNANCE  AND  GUNNERY. 

Consequently  in  seacoast  fortifications,  if  the  surroundings 
afford  convenient  sites  for  the  angle  measuring  instruments,  the 
range  finding  system  consists  of  two  transits  or  azimuth  instru- 
ments established  at  the  ends  of  a  long  base.  Observations  are 
made  on  the  target  from  both  ends  of  the  base.  The  position  of 
the  target  is  plotted  on  a  chart,  and  its  range  and  position  deter- 
mined for  any  gun.  If  the  target  is  moving,  simultaneous  obser- 
vations are  made  from  both  ends  of  the  base  at  periodic  intervals. 
The  readings  of  the  instruments  are  transmitted  by  telephone  or 
telegraph  to  a  plotting  room  in  the  fortification,  where  the  succes- 
sive positions  of  the  target  are  marked  on  the  chart.  From  the 
plotted  course  prediction  may  be  made  as  to  the  position  the 
target  will  occupy  at  some  determined  instant  in  advance,  and 
the  range  and  azimuth  of  the  target  at  the  selected  instant  may 
be  determined  for  any  gun  or  battery  in  the  fortification. 

300.  Depression  Range  Finders.-  The  principle  employed  in 
the  depression  range  finder  will  be  understood  from  Fig.  244. 

The  instrument,  at  a  known  height 
above  the  sea  level,  measures  the 
vertical  angle  to  any  object.     From 
F  the  fixed  height  each  angle  corre-. 

sponds  to  a  certain  length  of  base, 
which  is  the  horizontal  range  to  the  object. 

The  range  in  yards  is  indicated  on  a  scale  which  is  moved  past 
an  index  by  the  same  mechanism  that  gives  angular  movement  to 
the  line  of  sight. 

A  difference  in  the  sea  level  due  to  the  action  of  tides  will 
affect  the  height  of  the  instrument  above  the  sea  level  and  conse- 
quently the  range  corresponding  to  any  angle,  t  and  t',  Fig.  244. 
Means  are  therefore  provided  for  adjustment  of  the  instrument 
for  variations  in  its  height  above  sea  level. 

The  instrument  is  made  a  position  finder  by  being  mounted  so 
as  to  revolve  on  a  fixed  base  which  is  graduated  in  degrees  and 
hundred ths,  the  zero  graduation  being  placed  in  the  meridian 
plane. 

Swasey  Depression  Range  and  Position  Finder. — The  de- 
pression range  arid  position  finder  now  used  in  our  service  is  shown 
in  Fig.  245.  The  observing  telescope,  similar  in  construction  to 


*rj 

s 


O 

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3 


RANGE  AND   POSITION  FINDING.  527 

the  telescope  of  the  model  1904  sight,  is  mounted  in  a  frame  which 
revolves  about  a  central  spindle  s  projecting  upward  from  the 
pedestal.  The  telescope  is  pivoted  near  its  front  end,  and  is  sup- 
ported near  its  rear  end  by  the  attached  bar  v  which  rests  on  a  stu;l 
projecting  from  the  carriage  a.  The  carriage  a  is  mounted  on  the 
forward  arm  of  a  bent  lever  I  which  is  pivoted  at  o.  The  lower 
vertical  ami  of  the  lever  is  connected  by  gearing  with  the  operating 
shaft,  not  seen  in  the  figure.  Turning  the  operating  shaft  moves 
the  lower  end  of  the  lever  I,  and  thus  gives  vertical  movement  to 
the  telescope  about  its  forward  pivot.  The  range  drum  enclosed 
in  the  casing  d,  and  visible  through  the  window  w  in  the  casing, 
is  given  motion  by  the  same  shaft,  and  the  scale  on  the  drum  in- 
dicates the  range  corresponding  to  any  position  of  the  telescope. 
The  azimuth  is  read  from  a  graduated  scale  seen  through  the 
window  z. 

The  carriage  a  may  be  moved  along  the  upper  arm  of  the 
lever  to  adjust  the  position  of  the  telescope  for  any  height  above 
sea  level.  The  height  scale  along  which  the  carriage  moves  reads 
from  40  to  400  feet.  Corrections  may  be  made,  by  moving  the 
carriage,  for  the  change  in  height  of  the  instrument  due  to  the 
change  in  sea  level  caused  by  the  tides. 

301.  The  Plotting  Room. — The  range  and  azimuth  of  any  se- 
lected target,  as  determined  by  either  range  finder  system,  is  com- 
municated to  the  plotting  room.  In  this  room  are  assembled  all 
the  instruments  necessary  for  the  complete  determination  of  the 
elements  of  sighting  for  the  directing  gun  in  the  battery  wrhose  fire 
is  directed  from  the  room.  The  corrections  to  be  applied  to  the 
observed  range  to  compensate  for  the  effect  of  the  wind,  of  the 
thermometric  and  barometric  conditions,  of  differences  in  tide 
level,  and  of  the  motion  of  the  target,  are  quickly  determined  from 
the  instruments  for  a  predicted  position  of  the  target  at  some  in- 
stant in  advance.  The  deviation  due  to  the  wind  and  drift  and 
motion  of  the  target  are  also  determined.  The  corrected  range, 
azimuth,  and  deviation  are  sent  to  the  gun,  and  the  gun  is  then 
pointed  according  to  the  instructions  received.  The  command  to 
fire  is  given  at  such  a  moment  as  to  cause  the  shot  to  arrive  at  the 
predicted  position  of  the  target  at  the  same  instant  as  the  target. 

The  instruments  used  are  as  follows. 


528  ORDNANCE  AND  GUNNERY. 

The  wind  component  indicator  gives  the  components  of  the  wind 
for  range  and  deflection  for  use  on  the  range  and  deflection  boards. 
The  azimuth  of  the  wind's  direction,  taken  from  the  wind  dial,  and 
the  velocity  of  the  wind,  taken  from  an  anemometer,  are  laid  off 
on  the  instrument.  The  azimuth  of  the  target  is  also  laid  off,  and 
the  instrument  then  indicates  by  a  pointer  the  range  and  deflection 
components  of  the  wind  with  respect  to  the  line  from  the  gun  to 
the  target. 

The  atmosphere  board  indicates  the  correction  to  be  applied 
at  the  range  board  for  thermometric  and  barometric  changes. 

The  range  board,  with  the  data  supplied  by  the  foregoing  instru- 
ments and  other  data  indicated  below,  gives  the  correction's  in 
yards  to  be  applied  to  the  range  for  wind,  atmosphere,  tides,  and 
variations  from  the  standard  muzzle  velocity,  and  indicates  the 
sum  of  these  corrections. 

The  plotting  board  converts  the  range  and  position  of  the  target 
as  determined  from  the  reports  of  the  range  and  position  finders, 
to  the  range  and  position  for  the  particular  battery  or  gun,  with 
the  correction  for  range  determined  by  the  range  board. 

The  deflection  board  indicates,  for  the  corrected  range  and  azi- 
muth from  the  plotting  board,  the  sum  of  the  deflections  to  be 
applied  to  the  sight,  or  to  the  azimuth  of  the  piece,  to  correct  for 
the  deviating  effect  of  wind,  drift,  and  the  motion  of  the  target. 

By  means  of  these  instruments,  which  have  been  devised  by 
artillery  officers  of  our  army,  the  correct  setting  of  a  gun  may  be 
determined,  the  gun  aimed,  and  the  shot  sped  on  its  way,  in  an 
interval  of  15  seconds.  The  instruments  are  simple  in  construc- 
tion and  manipulation,  and  their  use  is  entrusted  to  the  enlisted 
soldier. 

302.  Field  Range  and  Position  Finding. — For  range  and  posi- 
tion finding  in  the  field  there  are  provided  the  Weldon  range  finder, 
the  battery  commander's  telescope,  the  battery  commander's 
ruler,  and  the  field  plotting  board.  The  uses  of  these  instruments 
will  be  understood  from  their  descriptions. 

The  Weldon  Range  Finder. — The  Weldon  range  finder,  Fig. 
246,  consists  of  three  triangular  prisms  mounted  in  a  metal  frame. 
The  silvered  base  of  each  prism  rests  against  the  metal.  The  angle 
at  the  apex  of  each  prism  is  as  follows. 


RANGE  AND  POSITION  FINDING. 


529 


The  upper  or  first  prism,  90  degrees 
The  second  prism,  88°  51'  15" 
The  third  prism,  74°  53'  15" 

Now  if  we  construct,  as  in  Fig.  247,  the  first  two  of  the  above 
angles  at  the  end  of  a  base  whose  length  is  unity,  and  the  third 


FIG.  247. 


FIG.  246. 


FIG.  248. 


angle  as  shown  in  the  figure,  the  sides  of  the  resulting  triangles  will 
be  of  the  lengths  marked  on  them  in  the  figure,  the  sides  being 
proprtional  to  the  sines  of  the  opposite  angles. 

Each  prism  diverts  a  ray  of  light  through  an  angle  equal  to  the 
angle  at  its  apex,  as  may  be  seen  from  Fig.  248.  A  ray  entering 
the  first  prism  from  I  or  a  issues  from  the  prism  in  a  direction  per- 
pendicular to  its  original  direction.  And.  similarly  a  ray  will  issue 
from  the  second  prism  at  an  angle  of  88°  51'  15"  with  its  original 
direction. 


530  ORDNANCE  AND  GUNNERY. 

Standing  at  a,  Fig.  249,  and  looking  into  the  first  prism,  we  see 
the  image  of  the  object  t  in  the  direction  ad,  perpendicular  to  at, 

and  at  the  same  time  looking  over 
the  prism  we  see  the  object  d  in  line 
with  the  image  of  t.  Now  moving 
back  on  the  line  da  there  will  be 
some  point  6  on  this  line  where  the 
target  t,  seen  in  the  second  prism, 

will  again  align  with  the  object  d  seen  over  the  prism.  The  angle 
tba  is  then  88°  51'  15"  and  at,  the  range  to  the  target,  is  50  times 
the  base  ab,  see  Fig.  247. 

The  second  prism  may  be  used  at  both  ends  of  the  base.  The 
triangle  abt  will  then  be  an  isosceles  triangle,  the  angle  at  a  being 
equal  to  the  angle  at  b,  and  the  length  of  the  sides  at  and  bt  will 
be  25  times  the  length  of  the  base. 

The  third  prism  is  provided  for  use  when  the  base  ab  is  incon- 
veniently long  or  when  through  the  interposition  of  a  gulch  or 
other  obstacle  the  length  of  the  base  can  not  be  directly 
measured. 

The  points  a  and  6,  Fig.  249,  having  been  determined,  the  ob- 
server moves  on  the  line  tb  to  some  point  c  from  which,  looking  in 
the  third  prism,  he  sees  the  image  of  the  point  a  covering  the  object 
at  t  seen  over  the  prism.  The  angle  at  c  is  then  74°  53"  15',  and 
as  shown  in  Fig.  247  the  base  cb  is  one  quarter  of  the  base  ab  or 
1/200  of  the  range  at. 

It  is  apparent  from  Fig.  248  that  the  instrument  may  be  used 
with  the  apex  of  the  prism  toward  the  eye  or  toward  the  target, 
since  both  t  and  a  may  represent  either  target  or  eye.  The  posi- 
tion of  the  image  in  either  case  with  respect  to  the  apex  of  the 
prism  is  indicated  in  the  figure. 

The  true  refracted  in:age  may  always  be  distinguished  from  im- 
ages reflected  from  the  face  of  a  prism  by  revolving  the  instrument 
about  a  vertical  axis.  Reflected  images  revolve  with  the  instru- 
ment, but  as  the  lateral  refraction  is  a  fixed  one  the  refracted  image 
remains  stationary  when  the  instrument  is  revolved. 

When  the  instrument  is  held  with  the  compass  needle  pointing 
north,  the  bottoms  of  the  two  notches  in  the  middle  of  the  cover 
mark  the  east  and  west  line;  and  these  two  notches  together  with 


RANGE  AND  POSITION  FINDING. 


531 


the  two  at  the  end  of  the  cover  mark  diagonal  lines  running  north- 
east and  northwest. 

303.  The  Battery  Commander's  Telescope.— The  battery  com- 
mander's telescope,  Fig.  250,  is  mounted  on  a  tripod  in  the  same 


FIG.  250. 

manner  as  the  telescope  of  a  transit  instrument.  It  has  movement 
about  horizontal  and  vertical  axes.  The  amounts  of  the  move- 
ments about  the  axes  are  indicated  by  scales  graduated  to  6400ths 
of  the  circle,  or  mils,  corresponding  for  horizontal  movement  to 
the  deflection  scale  of  the  panoramic  sight,  and  for  vertical  move- 
ment to  the  clinometer  scale  of  the  range  quadrant. 

The  telescope  forms  an  erect  magnified  image  of  the  object. 
The  ray  of  light  enters  the  window  in  front  of  the  objective  prism, 
is  reflected  downward  by  this  prism,  which  is  one  of  total  reflection, 


532  ORDNANCE  AND  GUNNERY. 

passes  through  the  objective,  is  rectified  by  the  two  Porro  prisms, 
and  forms  the  image  in  the  plane  of  the  cross  hairs  in  front  of  the 
eyepiece. 

The  objective  has  a  clear  aperture  of  If  inches,  and  a  focal 
length  of  11  inches.  The  power  of  the  telescope  is  10,  and  the 
field  of  view  is  4  degrees. 

The  battery  commander's  telescope  is  used  for  measuring  both 
horizontal  and  vertical  angles ;  horizontal!)7,  the  azimuths  between 
the  target,  gun,  and  aiming  point,  the  azimuth  of  the  front  of  a 
hostile  position,  the  correction  in  azimuth  required  to  bring  the 
shots  from  a  battery  on  to  the  target;  and  vertically,  the  angle  of 
position  of  the  target,  the  correction  in  elevation  required  to  bring 
the  projectile  to  the  target  or  the  burst  of  the  shrapnel  to  the 
proper  height  above  the  target. 

304.  The  Battery  Commander's  Ruler. — The  battery  com- 
mander's ruler,  Figs.  251  and  252,  constructed  after  the  manner 
of  the  slide  rule,  provides  on  the  front,  Fig.  251,  a  scale  for  quickly 
measuring  azimuths  and  a  slide  rule  for  determining  the  height 
of  the  trajectory  in  mils  at  any  point  of  the  range,  and  on  the  back, 
Fig.  252,  a  table  of  parallaxes,  computed  for  a  base  of  20  yards,  for 
several  ranges  and  for  different  angles  of  obliquity  of  base  to 
range. 

The  instrument  is  of  brass  about  6  inches  long,  1  inch  wide,  and 
|  of  an  inch  thick. 

A  cord  about  2  feet  long  passes  through  a  hole  in  the  ruler. 
One  end  of  the  cord  is  fastened  to  a  button  on  the  observer's  coat 
so  that  when  the  ruler  is  held  out  until  the  cord  is  taut  the  ruler 
is  20  inches  from  the  observer's  eye. 

The  scales  on  either  edge  of  the  front  of  the  ruler  are  graduated 
to  read  azimuths  in  mils.  To  measure  any  angle  hi  azimuth,  as 
for  instance  from  the  target  to  the  aiming  point,  the  ruler  is  held 
horizontally  at  the  length  of  the  cord  with  the  zero  at  the  end 
marked  T  in  line  with  the  target.  The  azimuth  to  the  aiming 
point  is  indicated  on  the  scale  at  the  point  where  the  line  from  the 
eye  to  the  aiming  point  cuts  the  edge  of  the  ruler.  It  will  be  seen 
that  azimuths  to  the  right  of  the  target  read  from  0  to  300,  and 
azimuths  to  the  left  read  from  6100  to  6400,  corresponding  to  the 
deflection  scales  of  the  sights.  The  ruler  is  always  held  with  that 


RANGE  AND  POSITION  FINDING. 


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ORDNANCE  AND  GUNNERY. 


edge  up  that  will  give  a  reading  in  the  desired  direction  from  the 
mark  T  on  the  scale.  All  desired  azimuths  are  similarly  measured. 
The  ruler  will  be  used  for  these  measurements  when  the  more 
accurate  battery  commander's  telescope  is  not  at  hand. 

THE  SLIDE.— The  slide  and  the  adjacent  range  'scale  on  the 
ruler  provide  the  means  for  determining  the  height  of  the  trajectory 
in  mils  at  any  given  point  of  the  range.  This  information  may  be 
frequently  required  for  use  in  ascertaining  whether  an  intervening 
obstacle  such  as  a  hill,  or  woods,  or  a  tower,  will  interfere  with 
the  fire  at  a  given  target,  or  in  determining  the  extent  behind  the 
obstacle  that  is  masked  from  the  fire  of  the  gun.  The  slide  is 
graduated  in  mils  from  —24  through  0  to  +284.  The  adjacent 
range  scale  on  the  ruler  is  in  hundreds  of  yards. 

To  use  the  instrument,  first  determine  the  angle  of  position  of 
the  target,  in  mils,  by  the  battery  commander's  telescope  or  other- 
vise.  Move  the  slide  so  as  to  place  the  slide  graduation  that  in- 
dicates the  angle  of  position  of  the  target  over  the  range  of  the 
ol  stacle  as  indicated  on  the  range  scale.  The  height  of  the  tra- 
jectory at  the  obstacle,  in  mils,  is  then  indicated  on  the  slide 
opposite  the  range  of  the  target  on  the  range  scale.  If  the  height 
indicated  is  greater  than  the  angle  of  position  of  the  obstacle, 
obtained  in  the  same  manner  as  the  angle  of  position  of  the  target, 
the  projectile  will  clear  the  obstacle. 

The  principle  involved  in  the  use  of  the  slide  will  be  under- 
stood from  Fig.  253,  in  which  the  6000-yard  trajectory  of  the  3- 


FIG.  253. 


inch  rifle  is  represented.  The  angular  heights  of  the  successive 
points  of  the  trajectory,  measured  from  the  origin,  evidently 
diminish  from  the  angle  of  departure  <j>  at  the  origin  to  zero  at  the 
end  of  the  range.  Under  the  principle  of  the  rigidity  of  the  tra- 


RANGE  AND   POSITION  FINDING.  535 

jectory  we  may  assume  with  sufficient  exactness  that  within,  the 
limits  of  direct  fire  any  portion  of  the  trajectory  from  the  origin  is 
the  true  trajectory  for  the  range  represented  by  its  chord.  We 
may  therefore  assume  the  portion  of  the  trajectory  subtended  by 
the  shorter  chord  in  the  figure  as  the  true  trajectory  for  the  range 
3200  yards,  and  from  the  figure  we  see  that  the  angular  height  of 
the  6000-yard  trajectory  at  3200  yards  is  the  angle  of  departure 
$  for  6000  yards  minus  the  angle  of  departure  c.7  for  3200  yards. 

On  the  range  scale  under  the  slide,  Fig.  251,  the  zero  of  the  two 
scales  being  together,  each  range  is  indicated  opposite  its  corre- 
sponding angle  of  departure  as  indicated  in  mils  on  the  slide. 
Thus  the  angle  of  departure  for  a  range  of  3200  yards  is  nearly  100 
mils,  100/6400  of  360  degrees,  or  5°  37'. 

A  movement  of  the  slide  in  either  direction  will  cause  the  read- 
ing above  any  range  to  be  increased  or  diminished,  that  is,  the 
movement  adds  an  angle  to  the  angle  of  departure  for  the  range, 
or  subtracts  an  angle.  If  the  zero  of  the  slide  is  moved  to  the 
3200-yard  mark  on  the  range  scale,  the  angle  of  departure  for 
3200  yards  is  subtracted  from  the  reading  over  every  range  on 
the  scale.  Therefore  the  angle  of  departure  for,  say,  the  6000- 
yard  range  is  diminished  by  the  angle  of  departure  for  3200  yards, 
and  as  shown  in  Fig.  253  this  difference,  indicated  on  the  slide 
over  the  6000-yard  mark  on  the  range  scale,  is  the  height  of  the 
6000-yard  trajectory  at  3200  yards. 

Now  if  we  assume  that  the  line  od,  Fig.  253,  is  horizontal  and 
that  the  target  at  c  is  elevated  above  d  by  the  angle  of  position  s, 
say  20  mils,  it  is  evident  that  20  mils  must  be  added  to  every 
reading  on  the  slide.  We  therefore  move  the  zero  of  the  slide  back 
until  the  20  on  the  slide  instead  of  the  zero  is  now  over  the  range 
3200.  The  reading  over  every  range  is  increased  by  20. 

We  have  now  put  the  angle  of  position  of  the  target  over  the 
range  of  the  obstacle,  and  over  the  range  of  the  target  we  read  the 
height  of  the  trajectory  at  the  obstacle. 

305.  THE  PARALLAX  TABLE.-  On  the  back  of  the  ruler,  Fig. 
252,  is  inscribed  what  is  called  the  parallax  table.  By  parallax  is 
meant  here  the  angle,  in  mils,  subtended  by  the  front  of  a 
platoon,  20  yards,  from  any  point  outside  the  battery.  Thus 
in  Fig.  254,  a  being  the  aiming  point  and  t  the  target,  the 


536  ORDNANCE  AND  GUNNERY. 

parallax  of  the  aiming  point  is  the  angle  at  a  subtended  by  the 
two  guns,  and  the  parallax  of  the  target  is  the  angle  at  t  sub- 
tended by  the  guns. 

The  parallax  of  a  point  that 
lies  in  a  direction  normal  to  the 
front  of  the  battery  is,  since  1 
mil  is  1/1000  of  the  range,  equal 
to  20  divided  by  the  number  of 
thousands  of  yards  in  the  range. 
Thus  for  4000  yards  the  parallax 
is  5  mils.  If  the  point  lies  in  a 

direction  oblique  to  the  front  of  the  battery,  the  parallax  is  equal 
to  the  normal  parallax  multiplied  by  the  cosine  of  the  angle  Avhich 
the  direction  of  the  point  makes  with  the  normal  to  the  battery 
front. 

The  parallax  has  been  calculated  for  different  ranges  and 
different  directions  of  the  point  and  tabulated  on  the  back  of  the 
ruler.  The  upper  two  lines  of  the  table,  Fig.  252,  give  the  angles 
of  obliquity  in  hundreds  of  mils  in  the  two  quadrants  in  front  of 
the  battery,  the  lower  two  lines  give  similar  angles  for  the  two 
quadrants  in  rear.  The  parallax  of  any  point  at  any  one  of  the 
four  ranges  marked  at  the  left  is  found  in  the  line  of  the  range  and 
in  the  column  that  indicates,  to  the  nearest  hundred  mils,  the 
obliquity  of  the  point's  direction.  The  parallax  in  any  fixed 
direction  is  an  inverse  function  of  the  range,  therefore  for  any 
range  not  given  in  the  table  it  may  be  readily  determined  by  means 
of  the  parallax  for  some  range  in  the  table.  Thus  the  parallax  for 
3000  yards  is  half  that  for  1500  yards  or  f  that  for  1000  yards. 

By  means  of  the  parallax  the  proper  setting  of  the  sight  in  in- 
direct firing  may  be  determined  for  one  gun  from  the  sighting  of 
the  adjacent  gun.  Thus  in  Fig.  254  if  the  gun  on  the  right  has 
found  the  target,  at  the  angle  a  from  the  aiming  point,  the  angle 
/?  for  the  second  gun  is  readily  obtained.  Representing  by  pa  and 
pt  the  parallax  angles  at  a  and  t  respectively,  we  see  from  the  figure 
that,  since 


RANGE  AND  POSITION  FINDING. 


537 


306.  Plotting  Board  for  Mobile  Artillery.— The  plotting  board, 
Fig.  255,  16  inches  wide  by  39  inches  long,  is  covered  with  rubber 
cloth.  Across  the  middle  of  the  board  is  a  grooved  guideway  g, 
its  edges  graduated  in  yards.  The  protractor  o  slides  in  the  guide- 
way.  The  protractor  is  graduated  in  64ths  of  a  circle  and  by  a 
vernier  may  be  read  to  mils.  The  outer  graduated  rim  of  the 
protractor  turns  about  the  fixed  central  part.  Fixed  to  the  outer 
rim  of  the  protractor  is  the  arm  /,  and  pivoted  to  the  center  of  the 
protractor  is  the  arm  m,  both  graduated  in  yards.  On  each  arm 


rCV=- 


FIG.  255. 

is  a  sliding  index,  a  and  t,  provided  with  a  pin  which  may  be 
stuck  into  the  board  to  hold  the  index  in  a  fixed  position. 

The  plotting  board  is  used  at  the  observing  station  to  deter- 
mine, for  the  directing  gun,  the  position  of  the  target  with  respect 
to  the  point  selected  as  an  aiming  point.  Thus  in  Fig.  254,  o  is 
the  observing  point  from  which  the  aiming  point  a,  the  target  /, 
and  the  directing  gun  are  visible.  The  ranges  from  the  observer 
to  the  three  points  are  determined,  and  the  angles  made  by  the 
lines  to  the  points  with  the  line  from  the  observer  to  the  gun. 
•This  line  to  the  gun  is  the  datum  line,  and  is  represented  on  the 
plotting  board  by  the  center  line  of  the  grooved  guideway.  The 
scale  on  the  edge  of  the  guideway  is  graduated  to  yards. 

With  the  protractor  in  the  center  of  the  board,  o  Fig.  255,  the 
arm  m  is  placed  at  an  angle  with  the  guideway  equal  to  the  angle 
d+  e,  Fig.  254,  and  the  sliding  index  on  the  arm  is  placed  at  the 
range  oa  on  the  scale.  Similarly  the  arm  /  is  revolved  to  make  the 
angle  d  with  the  guideway,  and  its  index  is  placed  at  the  range  ot 
on  the  scale.  The  pins  of  the  two  indexes  are  stuck  into  the  board. 

The  protractor  is  now  moved  along  the  guideway  to  the  point 


538  ORDNANCE  AND  GUNNERY. 

on  the  guideway  scale,  o'  Fig.  255,  that  marks  the  distance 
from  the  observer  to  the  gun.  The  two  arms  slide  through  the 
indexes  and  assume  the  positions  of  the  lines  from  the  gun  to  the 
aiming  point  and  to  the  target,  Fig.  254.  The  angle  a  between 
the  arms  is  read  from  the  protractor,  and  the  ranges  from  the  gun 
to  the  aiming  point  arid  target  are  read  from  the  scales  on  the 
arms. 

307.  Other  Range  Finders.  —  Other  range  finders  have  been 
constructed  on  the  principle  of  the  Weldon  range  finder,  using 
prisms  with  different  angles  or  producing  the  deflection  of  the  ray 
by  means  of  mirrors. 

The  Berdan  Range  Finder.  —  The  Berdan  range  finder  consists  of 
two  telescopes  permanently  mounted  6  or  12  feet  apart  on  the  bed  of 
a  wagon,  and  provided  with  graduated  circular  bases  by  means  of 
which  the  angles  between  each  of  the  telescopes  and  the  base  are 
measured.  The  short  base  renders  excessive  the  effect  of  a  slight 
error  in  the  measurement  of  an  angle,  and  for  this  reason  prin- 
cipally the  instrument  has  not  been  found  satisfactory  in  service. 

The  Barr  and  Stroud  Range  Finder.  —  The  Barr  and  Stroud 
range  finder,  used  on  the  ships  of  our  own  and  foreign  navies,  and 
now  being  tested  for  our  field  service,  is  constructed,  optically,  in 
the  manner  shown  in  Fig.  256.  The  tube  containing  the  optical 

I  \  ! 

>  i 

u 

A 

/  \! 

7=C  -  D 


t    f 
i 

FIG.  256. 

parts  is  so  mounted  on  the  deck  of  the  ship,  that  the  target  may  be 
kept  in  view  during  heavy  rolling  or  pitching  of  the  ship. 

Two  reflectors  r,  marking  the  ends  of  a  base  line  4£  feet  long, 
divert  the  rays  from  the  target  through  the  objectives  o  and 
thence  through  the  prisms  p  to  the  observer's  right  eye  at  e.  The 
field  of  view  of  the  right  eyepiece  is  divided  horizontally  by  a  dark 


RANGE  AND  POSITION   FINDING. 


539 


line,  Figs.  258  and  259.    The  image  from  the  objective  on  the 
right  is  formed  above  this  line  and  that  from  the  left  below  it. 

A  deflecting  prism,  d  Fig.  256,  has  a  sliding  movement  in  the 
right  telescope.  When  in  position  at  d  the  prism  has  no  deflecting 
effect  on  the  ray  from  the  objective,  and  in  this  position  of  the 
prism  the  parallel  rays  a  from  an  object  at  a  great  distance,  as 
from  the  sun  or  moon,  will  form  a  continuous  image  in  the  field  of 
the  right  eyepiece.  Now  if  a  nearer  object,  on  the  same  line  from 
the  left  reflector,  be  viewed,  the  direction  of  the  ray  to  the  light 
reflector  will  be  changed  from  a  to  s  and  the  image  from  the  righ, 
telescope  will  not  be  continuous  with  that  from  the  left,  Fig.  259. 


FIG.  257. 


FIG.  258. 


FIG.  259. 


FIG.  260. 


Continuity  in  the  image  is  obtained  by  sliding  the  deflecting 
prism  d  to  the  position  c.  The  amount  of  the  movement  of  the 
deflecting  prism  is  dependent  on  the  range  to  the  object;  and  the 
ranges  corresponding  to  the  various  positions  of  the  prism  are 
marked  on  a  scale  that  is  carried  by  the  prism.  A  movement  of 
the  deflecting  prism  over  a  length  of  six  inches  corresponds  to  a 
change  in  range  from  infinity  to  250  yards. 

The  observer  looks  with  his  left  eye  through  the  eyepiece  I, 
Fig.  256,  and  through  the  finder  objective  /  opposite.  The  left 
eyepiece  and  the  object  lens  /  form  a  low  powered  telescope  with 
a  large  field  of  view.  The  object  viewed,  Fig.  257,  is  seen  through 
this  telescope,  and  in  the  field  of  view  above  the  object  appear  a 
pointer  and  a  portion  of  the  scale  that  is  attached  to  the  deflecting 
prism  d.  The  range  to  the  object  is  read  from  the  scale  at  the 
pointer. 

For  use  at  night  in  obtaining  the  range  to  any  target  that  bears 
a  light  an  optical  appliance  called  an  astigmatizer  is  provided  in 
the  instrument.  The  astigmatizer  lengthens  the  images  of  a  point 
of  light  into  vertical  streaks,  Fig.  260,  and  the  streaks  are  brought 


540  ORDNANCE  AND  GUNNERY. 

into  coincidence.  The  astigmatizer  is  moved  aside  when  not  in 
use. 

The  Le  Bouleng6  Telemeter. — The  Le  Boulenge  telemeter  is 
an  instrument  by  means  of  which  the  velocity  of  sound  is  used  for 
measuring  distance.  The  instrument  is  a  glass  tube  filled  with 
liquid.  In  the  tube  is  a  loose  glass  piece  or  traveler  whose  specific 
gravity  is  but  slightly  greater  than  that  of  the  liquid,  so  that  when 
the  tube  is  held  vertical  the  traveler  falls  through  the  liquid  slowly 
and  with  approximately  uniform  motion.  The  time  between  the 
flash  of  a  gun  and  the  arrival  of  the  report  is  measured  by  turning 
the  tube  from  a  horizontal  to  a  vertical  position  when  the  flash  is 
seen,  and  back  to  the  horizontal  when  the  report  is  heard.  The 
range  corresponding  to  the  distance  that  the  traveler  has  fallen 
in  the  interval  is  read  from  a  scale  on  the  tube. 

As  the  velocity  of  sound,  1100  feet  per  second  in  cairn  air, 
varies  with  the  velocity  and  direction  of  the  wind,  this  method  of 
measuring  ranges  is  not  satisfactory. 


CHAPTER  XV. 
SMALL  ARMS  AND  THEIR  AMMUNITION. 

308.  Service  Small  Arms. — The  present  service  small  arms 
are  the  .38  caliber  revolver,  model  1903,  and  the  .30  caliber  rifle, 
model  1903.  Automatic  pistols  have  been  issued  to  the  service 
for  trial  within  recent  years,  but  the  results  of  the  trials  have  not 
been  sufficiently  favorable  to  bring  about  the  adoption  of  any  of 
these  arms  for  the  military  service.  Automatic  and  semi-auto- 
matic rifles  have  also  been  submitted  to  the  Ordnance  Depart- 
ment for  test.  The  tests  are  now  in  progress. 

The  .38  Caliber  Revolver. — The  service  revolver  is  made  by  the 
Colt's  Patent  Fire  Arms  Manufacturing  Co.  of  Hartford,  Conn.,  and 
is  known  as  the  Colt's  double  action  revolver,  caliber  .38. 

A  double  action  revolver  is  one  that  may  be  fired  in  either  of 
two  ways:  by  separately  cocking  the  hammer  and  pulling  the 
trigger,  or  by  performing  both  operations  with  a  single  pull  on  the 
trigger.  When  the  separate  movements  are  employed  the  piece 
is  said  to  be  used  in  single  action;  and  in  double  action,  when 
cocked  and  fired  by  the  pull  on  the  trigger  alone.  The  service 
revolver  may  be  used  either  in  single  action  or  in  double  action. 
Much  greater  rapidity  of  fire  can  be  attained  using  the  revolver  in 
double  action,  but  on  account  of  the  increased  effort  required  in 
firing  in  this  manner,  and  the  consequent  unsteadiness  of  the 
hand  holding  the  revolver,  the  fire  is  not  likely  to  be  as  accurate 
as  when  the  revolver  is  fired  in  single  action. 

The  mechanism  of  the  revolver  is  shown  in  Fig.  261.  The 
operation  of  the  mechanism  is  briefly  as  follows.  In  single  action 

541 


542 


ORDNANCE  AND  GUNNERY. 


the  piece  is  cocked  by  pressure  of  the  thumb  on  the  head  of  the 
hammer,  18.  The  lower  end  of  the  hammer  moves  the  upper 
end  of  the  trigger  forward  and  upward  until  the  upper  edge  of 
the  trigger  engages  under  the  lip  at  the  lower  end  of  the  hammer 
and  holds  the  hammer  in  the  cocked  position.  A  pull  on  the 
trigger  will  then  release  the  hammer,  which,  under  the  action  of 
the  mainspring  32,  falls  and  explodes  the  cartridge.  The  pressure 
on  the  trigger  being  released,  the  rebound-lever  spring  37 


FIG.  261. 


acting  on  the  rebound-lever  34  moves  the  hammer  back  slightly 
to  its  safety  position  and  at  the  same  time  moves  the  trigger 
forward. 

When  firing  in  double  action  the  pull  on  the  trigger  causes  the 
upper  end  of  the  trigger  to  bear  against  the  end  of  the  strut  10 
which  is  pivoted  on  the  pivot  of  the  hammer  and  bears  against  the 
hammer  above  the  pivot.  The  pull  on  the  trigger  thus  lifts  the 
hammer  until,  when  the  hammer  is  nearly  at  full  cock,  the  strut 
escapes  from  the  end  of  the  trigger  and  the  hammer  falls.  As 
the  rear  part  of  the  trigger  moves  upward,  whether  in  single  or 
in  double  action,  the  upper  end  of  the  hand  25  engages  in  a  notch 
on  the  rear  face  of  the  cylinder  and  causes  the  cylinder  to  revolve 
through  one-sixth  of  a  turn.  At  the  last  part  of  the  movement 


SMALL  ARMS  AND   THEIR  AMMUNITION.  543 

of  the  trigger  a  projecting  lug  forward  on  its  upper  surface  passes 
through  a  slot  in  the  frame  and  engaging  in  a  notch  in  the  cylinder 
prevents  further  movement  of  the  cylinder. 

The  mechanism  includes  safety  devices  which  allow  the  piece 
to  be  cocked  only  when  the  cylinder  is  fully  closed  and  latched  in 
the  proper  position. 

309.  THE  MAINSPRING  TENSION  SCREW. — The  mainspring  ten- 
sion screw  33  is  an  important  part  of  the  mechanism  whose  func- 
tions are  not  usually  understood.  Its  purpose  is  to  vary  the  ten- 
sion of  the  mainspring  in  order  to  adjust  the  force  of  the  blow 
delivered  by  the  hammer  on  the  primer  of  the  cartridge.  When 
the  revolver  is  used  in  double  action  the  hammer  is  not  retracted 
as  far  as  in  single  action  and  consequently  delivers  a  lighter  blow 
on  the  primer.  It  is  a  difficult  matter  to  manufacture  a  primer 
suitable  for  both  methods  of  firing.  If  the  cap  of  the  primer  is 
made  thin  enough  to  insure  firing  of  the  primer  under  the  lighter 
blow  in  double  action,  the  metal  of  the  cap  is  likely  to  be  pierced 
by  the  point  of  the  hammer  under  the  heavier  blow  in  single 
action.  The  pierced  primer  allows  the  powder  gases  to  escape  to 
the  rear,  perhaps  to  the  injury  of  the  soldier.  If  on  the  other 
hand  the  primer  cap  be  made  sufficiently  thick  to  insure  its  not 
being  punctured  by  the  heavier  blow,  the  primer  may  not  be 
sufficiently  sensitive  to  be  always  fired  by  the  lighter  blow.  The 
importance  of  a  proper  adjustment  of  the  tension  of  the  main- 
spring is  therefore  apparent.  If  it  is  found  that  failures  to  fire  in 
double  action  are  frequent  the  screw  33  should  be  screwed  in 
slightly  to  increase  the  tension  of  the  mainspring  and  produce  a 
heavier  blow  of  the  hammer.  But  the  tension  must  not  be  in- 
creased more  than  absolutely  necessary,  for  otherwise  puncture 
of  the  primer  may  occur  when  the  revolver  is  fired  in  single 
action. 

THE  BARREL. — The  barrel  of  the  revolver  has  a  length  of  6 
inches,  and  a  diameter  between  the  lands  of  the  rifled  bore  of 
0.357  of  an  inch.  It  is  rifled  with  6  grooves  0.003  of  an  inch  deep 
and  with  a  uniform  twist  of  one  turn  in  16  inches.  The  rifling  has 
a  left  handed  twist  in  order  that  the  drift  of  the  bullet  to  the  left 
may  counteract  to  some  extent  the  tendency  that  exists  to  pull 
to  the  right  in  firing. 


544  ORDNANCE  AND  GUNNERY. 

AMMUNITION  AND  BALLISTICS. — The  ball  and  blank  cartridges 
used  in  the  revolver  are  shown  in  Fig.  262.  The  charge  in  the 
ball  cartridge  is  about  3£  grains  of  a  nitroglycerine  powder,  and 
produces  in  the  bullet  a  muzzle  velocity  of  750 
feet.  The  bullet,  of  lead,  weighs  148  grains. 
Its  greatest  diameter  is  0.357  of  an  inch,  which 
is  the  diameter  between  the  lands  of  the  rifled 
bore.  The  powder  gases  entering  a  conical 
cavity  in  the  base  of  the  bullet  expand  the 
base  of  the  bullet  into  the  grooves  of  the  rifling. 
The  grooves  of  the  bullet  are  filled  with  Japan 
wax  as  a  lubricant.  The  wax  also  serves,  to- 

FIG.   262.  .        . 

getner  with  the  crimping  of  the  front  end 
of  the  cartridge  case  against  the  bullet,  to  keep  out  moisture  and 
render  the  cartridge  waterproof. 

While  the  bullet  has  sufficient  energy  to  inflict  a  disabling 
wound  at  a  range  of  200  yards,  the  revolver  cannot  be  relied  upon 
for  accurate  firing  beyond  75  yards. 

The  blank  cartridge  contains  7  grains  of  E.  C.  powder  held  hi 
the  case  by  a  paper  wad  crimped  in  place  and  shellacked. 

310.  The  Colt  Automatic  Pistol. — In  the  Colt  automatic 
pistol  the  recoil  of  a  movable  barrel  and  slide  is  utilized  to  eject 
the  fired  shell,  cock  the  firing  mechanism,  and  load  a  new  car- 
tridge into  the  barrel;  so  that  after  the  first  shot  is  fired  the  only 
operation  necessary  to  fire  the  remaining  cartridges  in  the  maga- 
zine is  a  pull  of  the  trigger  for  each  cartridge. 

The  pistol  is  made  in  three  calibers,  .32,  .38,  and  .45.  The 
magazines  of  the  two  smaller  pistols  hold  8  cartridges;  that  of 
the  .45  caliber  pistol  holds  7  cartridges.  The  .45  caliber  pistol  is 
represented  in  Figs.  263  to  265.  The  rear  part  of  the  frame  or 
receiver  r  forms  a  hollow  handle  which  encloses  the  magazine 
and  the  firing  mechanism.  The  magazine,  Fig.  264,  is  a  light  metal 
case  containing  a  spring  and  follower.  The  cartridges  are  in- 
serted one  at  a  time  by  sliding  in  at  the  top.  The  sides  of  the 
magazine  curve  slightly  over  the  upper  cartridge,  which  may  be 
removed  only  by  being  pushed  out  to  the  front.  The  magazine 
when  filled  is  inserted  into  the  handle  of  the  pistol  from  below 
and  is  held  in  place  by  a  spring  catch. 


FIG.  265. 
Colt  Automatic  Pistol,  Caliber  .45. 


SMALL  ARMS  AND   THEIR  AMMUNITION.  545 

The  forward  extension  of  the  receiver  r  contains  the  retractor 
spring  g  and  has  formed  on  its  sides  guides  for  the  reciprocating 
slide  s.  The  barrel  b  is  attached  to  the  receiver  by  two  links  o. 
The  forward  part  of  the  slide  s  covers  the  barrel,  and  the  rear 
part  forms  the  breech  bolt  and  carries  the  firing  pin.  Three  lugs 
formed  on  the  top  of  the  barrel  engage  in  notches  in  the  slide  and 
lock  barrel  and  slide  together.  The  slide  lock  c,  a  straight  bar, 
holds  the  slide  to  the  receiver.  It  passes  through  longitudinal 
slots  in  the  sides  of  the  receiver,  and  its  ends  are  engaged  in 
notches  in  the  slide.  The  head  of  the  retractor-spring  follower 
/  presses  against  a  recessed  seat  in  the  middle  of  the  slide  lock 
c,  and  thus  holds  slide  and  barrel  in  firing  position. 

OPERATION. — The  operation  of  the  pistol  when  fired  is  as 
follows.  The  powder  gases  acting  rearwardly  against  the  bolt 
force  the  slide  to  the  rear  against  the  pressure  of  the  retractor 
spring.  The  barrel,  carried  to  the  rear  with  the  slide,  revolves 
about  the  lower  pivots  of  the  two  links  o,  its  axis  always  remain- 
ing parallel  to  the  top  of  the  receiver.  The  downward  movement 
of  the  barrel  soon  disengages  it  from  the  slide,  but  not  until  after 
the  bullet  has  left  the  muzzle.  The  momentum  acquired  by  the 
slide  causes  it  to  continue  to  the  rear.  Its  rear  end  cocks  the 
hammer  h.  An  extractor  carried  by  the  slide  withdraws  the 
fired  shell  which,  striking  an  ejector,  is  throwrn  out  to  the  right 
through  a  slot  in  the  slide.  When  the  front  of  the  bolt  has  passed 
to  the  rear  of  the  top  cartridge  in  the  magazine  this  cartridge  is 
forced  upward  into  the  path  of  the  bolt  by  the  magazine 
spring. 

As  the  slide  returns  under  the  action  of  the  retractor  spring 
the  bolt  forces  the  top  cartridge  forward  out  of  the  magazine 
into  the  barrel  in  its  lowrered  position,  and  then  raises  the  barrel 
into  its  locked  position  for  firing.  A  pull  on  the  trigger  now  causes 
the  cocked  hammer  to  strike  the  firing  pin  and  fire  the  cartridge. 

When  the  last  cartridge  has  been  fired  the  slide  remains  to  the 
rear,  thus  warning  the  soldier  that  the  magazine  is  empty. 

The  safety  lever,  /  Fig.  263,  prevents  movement  of  the  trigger 
until  the  slide  and  barrel  are  in  proper  position  for  firing. 

To  load  the  first  cartridge  into  the  barrel,  the  rearward  move- 
ment of  the  slide  is  produced  by  hand,  the  slide  being  grasped  by 


546  ORDftAXCE  AND  GUNNERY 

the  disengaged  hand  at  the  roughened  surfaces  on  its  sides,  and 
pulled  to  the  rear. 

The  necessity  of  using  two  hands  to  load  the  first  cartridge  into 
the  barrel  is  one  objection  to  the  pistol  as  a  military  arm. 

HOI.STER. — The  pistol  holster  is  a  light  steel  frame  covered  v,  ith 
leather,  and  is  arranged  to  be  attached  to  the  butt  of  the  pistol 
in  such  a  manner  as  to  serve  as  a  stock  by  means  of  which  the 
pistol  can  be  fired  from  the  shoulder. 

AMMUNITION. — The  .45  caliber  bullet,  of  lead  with  a  cupro 
nickel  jacket,  weighs  200  grains.     The  charge  of  powder  is  5.1 
grains.    The  muzzle  velocity  of  the  bullet  is  900  feet. 

Five  shots  ma)7  be  fired  from  the  pistol  in  a  second . 

311.  Modern  Military  Rifles. — The  modern  military  rifle 
differs  from  its  predecessors  chiefly  in  caliber  and  in  the  use  of 
the  magazine.  The  caliber  of  the  rifle  in  our  service  has  been 
reduced  from  0.45  to  0.30  of  an  inch,  with  an  accompanying  reduc- 
tion in  the  weight  of  the  bullet  from  500  grains  to  220  grains,  and 
recently  to  150  grains.  The  maximum  pressure  in  the  bore  has 
been  increased,  with  the  change  in  caliber,  from  25,000  pounds 
per  square  inch  to  44,000  pounds. 

INCREASED  VELOCITY. — The  increased  pressure,  better  sus- 
tained along  the  bore  by  modern  powders,  produces  in  the  lighter 
bullet  a  velocity  very  much  greater  than  that  attained  in  the 
rifles  of  larger  caliber.  The  muzzle  velocity  of  the  bullet  from 
the  .45  caliber  rifle  was  1300  feet  per  second,  while  the  present 
sendee  rifle  gives  to  the  220-grain  bullet  a  muzzle  velocity  of  2200 
feet,  and  to  the  150-grain  bullet  a  muzzle  velocity  of  2800  feet. 
At  the  same  time,  since  the  weight  of  the  gun  has  not  materially 
changed,  the  ratio  of  weight  of  bullet  to  weight  of  gun  has  greatly 
diminished.  On  this  ratio  principally  depends  the  maximum 
velocity  of  free  recoil  of  the  gun  for  any  given  velocity  of  the 
projectile,  see  equation  (4),  page  275.  We  may  consider  the 
velocity  of  recoil,  or  better  its  square,  as  a  measure  of  the  shock 
of  recoil.  In  the  modern  rifle  the  ratio  of  weight  of  bullet  to 
weight  of  gun  is  diminished  to  such  an  extent  that,  even  with  the 
increased  velocity  of  the  bullet,  the  velocity  of  recoil  is  dimin- 
ished. In  consequence  of  the  lighter  shock  of  recoil  on  the  soldier's 
shoulder,  he  is  enabled  to  longer  continue  his  fire  without  fatigue. 


SMALL  ARMS  AND  THEIR  AMMUNITION.  547 

OTHER  ADVANTAGES.  —  The  increased  muzzle  velocity  in- 
creases the  range  and  accuracy  of  the  rifle  and  flattens  the  trajec- 
tory, thus  increasing  the  danger  space  for  any  range.  The  in- 
creased velocity  has  been  attained  with  a  shorter  barrel,  thus 
diminishing  the  weight  of  the  gun  and  facilitating  the  handling  of 
the  gun  by  the  soldier. 

The  reduced  weight  of  the  bullet  and  of  the  charge  of 
powder  reduces  the  weight  of  the  cartridge,  thereby  enabling 
the  soldier  to  carry  a  greater  number  of  cartridges  on  his 
person. 

THE  JACKETED  BULLET. — In  order  that  the  metal  of  the  bullet 
shall  not  be  stripped  by  the  rifling  as  the  bullet  passes  with  high 
velocity  through  the  bore,  it  is  necessary  to  cover  the  soft  lead  of 
the  bullet  with  a  jacket  of  tougher  material.  The  modern  bullet 
is  therefore  composed  of  a  lead  core  enclosed  in  a  jacket  made  of 
cupro-nickel  or  of  nickeled  steel.  The  leaxi  gives  weight  to  the 
bullet  and  increases  its  sectional  density,  see  page  458,  while  the 
tougher  jacket  enables  the  bullet  to  take  the  rifling  without  ma- 
terial deformation,  and  also  gives  to  the  bullet  greater  penetra- 
tion in  any  resisting  material. 

THE  MAGAZINE. — Ease  and  rapidity  of  fire  are  greatly  increased 
by  the  use  of  the  magazine.  At  the  first  introduction  of  magazine 
guns  the  cartridges  in  the  magazine  were  considered  as  in  reserve, 
to  be  used  only  in  cases  of  emergency.  The  gun  was  habitually 
used  as  a  single  loader.  In  the  latest  weapons  the  filling  of  the 
magazine  may  be  accomplished  more  readily  than  the  insertion 
of  a  single  cartridge  into  the  barrel,  since  the  cartridges  are  carried 
by  the  soldier  in  packets  adapted  to  magazine  loading  only.  Maga- 
zine fire  is  therefore  used  habitually,  though  the  guns  are  adapted 
for  single  loading  as  well. 

The  mechanism  of  the  magazine  is  usually  arranged  to  lock 
the  bolt  of  the  gun  open  when  the  magazine  is  empty,  so  that  in 
the  excitement  of  battle  the  soldier  may  not  continue  to  go  through 
the  motions  of  firing  with  an  unloaded  gun. 

312.  Requirements. — That  the  military  arm  may  stand  the 
rough  usage  incident  to  sendee  in  war  it  is  essential  that  it  be 
strongly  constructed.  Its  mechanisms  must  be  strong,  simple, 
and  easily  dismantled  for  repair  in  the  field  without  the  use  of 


548  ORDNANCE  AND  GUNNERY. 

tools.  Tho  mechanisms  must  not  be  seriously  affected  by  a  mod- 
erate amount  of  rust  or  dust. 

To  lessen  the  chances  of  injury  to  the  rifle  as  few  of  the  parts 
as  possible  should  project  beyond  its  general  outline.  This  latter 
consideration  forms  one  of  the  objections  to  the  attachment  to 
military  rifles  of  telescopic  sights  and  other  devices  for  increasing 
the  accuracy  of  fire.  The  military  rifle  can  rarely  get  the  care 
necessary  to  keep  the  more  delicate  and  more  complicated  sporting 
and  target  rifles  in  condition.  Especially  is  this  so  in  time  of  war 
when  armies,  those  of  the  United  States  particularly,  are  largely 
composed  of  untrained  volunteers  most  of  whom  have  never  pre- 
viously carried  a  rifle.  The  arm  that  is  put  into  their  hands  must  be 
of  such  a  character  that  it  will  be  serviceable  under  almost  all  con- 
ditions, and  as  accurate  as  it  ma}'  be  made  under  this  requirement. 

Tests. — Before  the  adoption  into  our  service  of  a  rifle  of  new 
model  the  arm  is  subjected  to  tests  as  follows. 

ENDURANCE  TEST. — The  arm  is  tested  for  endurance  by  firing 
from  each  of  several  rifles  5000  rounds,  in  forty  lots  of  100  rounds 
each  and  two  lots  of  500  rounds  each. 

At  various  stages  of  the  endurance  test  the  ballistic  qualities 
of  the  arm  are  tested  by  firing  for  velocity  and  accuracy,  and  the 
working  of  the  mechanism  by  tests  for  rapidity  of  fire. 

DUST  TEST. — The  rifle,  with  the  breech  block  closed,  is  sub- 
jected to  a  blast  of  fine  sand  for  two  minutes,  first  with  the  maga- 
zine empty  and  again  with  the  magazine  filled  with  cartridges. 
After  each  exposure  to  the  blast  the  surplus  sand  is  removed  by 
blowing,  by  wiping  with  the  bare  hands  only,  and  by  tapping  the 
butt  and  muzzle  on  the  ground.  The  rifle  must  then  be  capable  of 
operation  in  single  loading  and  in  magazine  fire. 

RUST  TEST. — The  rifle  is  thoroughly  cleaned  and  all  oil  and 
grease  removed  by  washing  in  soda  water.  The  muzzle  and 
chamber  are  tightly  corked  and  the  rifle  is  immersed  in  a  saturated 
solution  of  sal  ammoniac  for  ten  minutes  and  then  exposed  to  a 
damp  atmosphere  for  48  hours.  The  rifle  must  then  be  capable 
of  operation  as  before.  » 

DEFECTIVE  CARTRIDGE  TEST. — Cartridges  cut  through  at  the 
head,  others  cut  through  at  the  extractor  groove,  and  others  slit 
throughout  their  length  are  fired  in  the  rifle. 


s 

2. 
o 


W 


FIRED  FROM  NEW  BARREL  INTO  SAWDUST. 


FIRED  INTO  SAWDUST  FROM    BARREL    PREVIOUSLY 
FIRED  3500  TIMES. 


FIRED   INTO  SAWDUST   FROM   BARREL  PREVIOUSLY 
FIRED  4500  TIMES. 


FIG.  267. — Effects  of  Erosion  on  Bullets. 


SMALL  ARMS  AND  THEIR  AMMUNITION.  549 

EXCESSIVE  CHARGE  TEST. — Five  rounds  arc  fired  with  car- 
tridges loaded  to  produce  a  maximum  pressure  in  the  chamber 
one  third  greater  than  the  maximum  pressure  attained  in  service. 

313.  Life  of  the  Rifle.  Erosion. — Although  the  rifle  remains 
serviceable,  as  far  as  the  operation  of  its  mechanism  is  concerned, 
after  endurance  tests  of  5000  rounds  or  more,  its  accuracy  dimin- 
ishes markedly  after  a  number  of  rounds  considerably  less  than 
5000,  the  number  depending  on  the  conditions  of  the  firing.  With 
its  accuracy  seriously  impaired  the  rifle  ceases  to  be  suitable  for 
service.  The  service  life  of  the  rifle  must  therefore  be  measured 
by  the  number  of  rounds  that  can  be  fired  from  it  with  accuracy, 
and  not  by  the  number  fired  in  tests'  for  endurance. 

The  accuracjr  of  the  rifle  is  principally  affected  through  the 
erosion  of  the  barrel  by  the  powder  gases.  The  gases,  highly 
heated  and  moving  with  high  velocity  under  great  pressure,  at- 
tack the  walls  of  the  bore,  which  are  probably  softened  by  the 
great  heat,  and  cut  irregular  channels  in  the  metal,  destroying  the 
surface  of  the  bore  and  the  rifling.  The  erosion  is  greatest  at  the 
seat  of  the  bullet  immediately  in  front  of  the  cartridge  case,  and 
extends  forward  into  the  barrel  for  several  inches.  Beyond  this 
the  walls  of  the  bore  are  practically  unaffected. 

The  effect  of  erosion  is  well  shown  in  the  enlarged  photographs, 
Fig.  266,  of  rifle  barrels  from  which  3500,  4000,  and  5000  rounds 
have  been  fired. 

When  the  erosion  has  become  marked,  the  bullet  is  forced 
against  an  irregular  surface  and  the  metal  of  the  bullet  jacket, 
probably  also  softened  by  the  heat,  is  unequally  stretched  on 
different  sides,  producing  a  decided  eccentricity  of  the  point  of 
the  bullet  and  great  irregularity  of  the  base.  The  sides  of  the 
bullet  are  deeply  scored  by  the  powder  gases  escaping  past  the 
bullet  and  by  the  irregularities  of  the  bore. 

In  Fig.  267  are  shown  enlarged  photographs  of  a  service  220- 
grain  bullet,  model  1903,  recovered  after  being  fired  into  sawdust 
from  a  -new  rifle  barrel,  and  of  bullets  fired  from  barrels  that  had 
been  previously  fired  3500  and  4500  times. 

The  deformation  of  the  bullet  is  the  chief  cause  of  its  inaccuracy. 
At  the  same  time  its  muzzle  velocity  is  reduced  by  the  escape 
of  the  gases  past  the  bullet  in  the  bore. 


550  ORDNANCE    AND   GUNNERY. 

VELOCITY  AND  PRESSURE. — The  erosive  effect  of  the  gases  ap- 
pears to  depend  more  on  their  velocity  than  on  the  maximum 
pressure.  Thus  in  tests  that  were  made  with  the  service  rifle  with 
220-grain  bullets  fired  with  muzzle  velocities  of  2300  and  2200 
feet,  the  maximum  pressures  in  the  two  cases  not  being  very 
different,  the  first  appreciable  falling  off  in  accuracy  occurred 
after  2000  rounds  with  the  2300-foot  velocity  and  after  4000  rounds 
with  the  velocity  of  2200  feet;  and  the  accuracy  after  7000  rounds 
with  the  lower  velocity  was  better  than  after  4000  rounds  with  the 
higher. 

Ammunition  loaded  to  produce  a  muzzle  velocity  of  2300  feet 
was  originally  used  in  the  service  rifle,  but  after  the  above  men- 
tioned tests  the  muzzle  velocity  was  reduced  to  2200  feet  and  the 
accuracy  life  of  the  rifle  increased  from  2000  to  4000  rounds. 

The  150-grain  bullet  recently  adopted  for  the  new  rifle  was 
intended  originally  to  have  a  muzzle  velocity  of  2800  feet,  the 
maximum  pressure  being  considerably  less  than  with  the  220- 
grain  bullet.  It  is  doubtful  whether,  on  account  of  the  rapid 
erosion,  this  high  velocity  can  be  fixed  as  the  standard. 

Erosion,  the  cause  of  the  reduction  in  the  muzzle  velocity  in 
the  small  arm,  is  also  the  cause  of  the  recent  reduction  of  the 
muzzle  velocities  in  the  10-  and  12-inch  seacoast  guns  from  2500 
to  2250  feet. 

314.  The  U.  S.  Magazine  Rifle,  Model  1903.— The  present 
service  rifle  fulfils  all  the  requirements  enumerated  in  a  previous 
paragraph  as  essential  for  a  military  rifle.  As  the  Cadets  of  the 
Military  Academy  are  armed  with  the  rifle  and  familiar  with  its 
operation  through  daily  use,  an  extended  description  of  the 
weapon  is  not  necessary  here.  Consideration  of  some  of  its  parts 
may  be  of  advantage. 

Two  views  of  the  mechanism  of  the  rifle,  with  bolt  in  closed 
position,  are  shown  in  Fig.  268. 

THE  RECEIVER. — The  receiver  is  that  part  of  the  gun  that 
contains  the  breech  closing  bolt.  It  is  held  to  the  stock  by  the 
two  guard  screws,  front  and  rear.  The  barrel  is  screwed  into  the 
front  of  the  receiver. 

TRIGGER  PULL. — It  will  be  observed  that  the  rounded  upper 
edge  of  the  trigger  bears  against  the  bottom  of  the  rear  part  of  the 


SMALL  ARMS  AND   THEIR  AMMUNITION. 


551 


552  ORDNANCE  AND  GUNNERY. 

receiver,  against  which  it  is  held  by  the  pressure  of  the  sear  spring, 
the  trigger  being  pivoted  in  the  slotted  sear.  When  the  trigger  is 
pulled  it  has  comparatively  free  movement  until  the  rear  point, 
or  heel,  of  the  trigger  bears  against  the  receiver.  The  nose  of  the 
sear,  its  rear  part  which  projects  upward  through  a  slot  in  the  re- 
ceiver, is  by  this  movement  partially  withdrawn  from  the  sear  notch 
in  the  cocking  piece.  When  the  heel  of  the  trigger  bears  against 
the  receiver  the  trigger  leverage  is  reduced  and  a  short  but  more 
decided  pull  is  required  to  further  withdraw  the  sear  from  the 
sear  notch.  The  purpose  of  the  first  movement  of  the  trigger, 
against  slight  resistance,  is  to  prevent  accidental  discharge  of  the 
piece  as  the  soldier  first  feels  the  trigger,  and  to  increase  the  accu- 
racy of  fire  by  enabling  the  soldier  to  partially  withdraw  the  sear 
while  aiming,  and  to  complete  its  withdrawal  at  the  proper  mo- 
ment by  a  slight  movement  of  the  finger. 

CAMS. — In  the  operation  of  the  mechanism  the  most  decided 
resistances  are  encountered  in  the  compression  of  the  mainspring 
and,  at  times,  in  the  insertion  of  a  cartridge  into  the  barrel  and 
in  the  extraction  of  the  fired  shell.  In  orcier  that  these  opera- 
tions may  be  accomplished  with  the  least  fatigue  to  the  soldier 
they  are  all  performed  by  means  of  cams. 

The  mainspring  is  partially  compressed  in  the  movement  of 
unlocking  the  bolt  by  the  action  of  a  cammed  surface  of  the  bolt 
against  the  cocking  cam  on  the  firing  pin,  and  the  compression  of 
the  spring  is  completed  on  the  closing  of  the  bolt  by  the  action  of 
the  two  locking  lugs  at  front  end  of  bolt  against  the  cammed 
locking  shoulders  in  the  receiver.  The  cammed  movement  of 
rotation  also  forces  the  cartridge  to  its  seat  in  the  chamber.  In 
the  rotation  of  the  bolt  in  opening,  the  extracting  cam  at  upper 
end  of  bolt  handle  works  against  a  cammed  surface  in  the  receiver 
and  moves  the  bolt  slightly  to  the  rear,  starting  the  fired  shell 
from  the  chamber. 

THE  BARREL. — The  rifling  of  the  barrel  consists  of  four  grooves 
0.004  of  an  inch  deep.  The  grooves  are  three  times  as  wide  as 
the  lands.  The  twist  is  uniform,  one  turn  in  10  inches,  and  right 
handed.  The  length  of  the  barrel,  measured  from  end  to  end,  is 
24.206  inches,  a  length  that  permits  the  use  of  this  arm  by  the 
cavalry,  and  makes  their  fire  as  efficient  as  that  of  the  infantry. 


SMALL  ARMS  AND   THEIR  AMMUNITION.  553 

Formerly  the  cavalry  were  provided  with  carbines,  short  guns 
with  the  same  mechanism  as  the  longer  rifle  and  using  the  same 
ammunition. 

The  muzzle  of  the  barrel  is  rounded  to  protect  the  rifling. 
Any  irregularity  of  the  muzzle  end  of  the  bore  will  seriously  affect 
the  accuracy  of  the  arm  by  causing  unequal  pressure  on  the  sides 
of  the  bullet  as  it  is  about  to  leave  the  bore. 

315.  THE  SIGHTS,  MODEL  1905. — The  sight  seats  or  bases  for 
front  and  rear  sights  are  bands  that  encircle  the  barrel,  to  which 
they  are  fixed  by  splines  and  pins.  This  method  of  attachment 
is  preferable  to  the  method  formerly  employed  of  screwing  the 
sight  seats  directly  to  the  barrel,  as  the  sights  are  now  more  se- 
curely held  and  there  is  less  likelihood  of  their  adjustment  being 
disturbed. 

The  windage  screw,  Fig.  268,  which  gives  the  movement  in 
deflection  to  the  rear  sight,  is  acted  on  by  a  spring  which  prevents 
lost  motion  due  to  wear  in  the  parts  of  the  rotating  mechanism. 

Each  division  or  point  of  the  deflection  scale  of  the  rear  sight 
corresponds  to  a  lateral  deviation  of  4  inches  in  100  yards. 

The  leaf  of  the  sight  is  graduated  for  elevations  from  100  to 
2500  yards,  the  sight  for  the  latter  range  being  taken  through  the 
notch  on  upper  end  of  leaf. 

With  the  leaf  down  the  sights  are  set  at  400  yards,  battle  range, 
at  all  positions  of  the  slide  on  the  leaf. 

In  the  movement  of  the  slide  up  the  leaf,  the  drift  slide,  Fig. 
268,  in  which  are  cut  the  sighting  notches  and  peep,  follows  a 
drift  curve  cut  in  the  leaf  and  thus  compensates  for  the  lateral 
deviation  of  the  trajectory  from  the  line  of  sight  as  adjusted  on 
the  piece.  Explanation  of  the  drift  and  of  the  adjustment  of  the 
line  of  sight  will  be  found  in  a  later  paragraph  entitled  Deviation. 

The  front  sight  is  fitted  in  a  stud  that  before  being  screwed  to 
its  seat  is  adjusted  laterally  to  its  proper  position  on  the  indi- 
vidual rifle.  The  proper  adjustment  is  obtained  by  actual  firing 
with  each  rifle.  The  firings  are  done  by  expert  marksmen  over  a 
covered  200-yard  range  provided  at  the  armory. 

The  sight  radius  of  the  piece,  the  horizontal  distance  between 
the  point  of  the  front  sight  and  the  rear  edge  of  the  notch  or  peep 
of  the  rear  sight,  is  22.3251  inches, 


554 


ORDNANCE  AND  GUNNERY 


RAPIDITY  OF  FIRE. — With  single  loading, 
23  aimed  shots  have  been  fired  from  the  rifle 
in  one  minute,  and  with  magazine  fire,  25 
shots  in  one  minute.  With  the  rifle  held  at 
the  hip,  27  unaimed  shots,  loaded  singly,  have 
been  fired  in  one  minute,  and  with  magazine 
fire,  35  shots. 

THE  BAYONET. — The  tang  B  of  the  bay- 
onet, Fig.  209,  is  of  one  piece  with  the  blade. 
In  a  recess  in  the  tang  is  mounted  the  catch 
H  which  engages  under  the  bayonet  stud  on 
the  gun,  locking  the  bayonet  to  the  gun;  and 
the  catch  E  which  secures  the  bayonet  in  its 
scabbard  by  engaging  a  hook  provided  in  the 
scabbard .  Ei  ther  catch  is  released  by  pressure 
on  the  thumb  piece  E. 

Appendages. — Among  the  appendages 
provided  for  the  care  of  the  piece  is  a  bullet 
jacket  extractor, 
Fig.270,  a  cylin- 
drical steel  plug 
rifled  on  the  ex- 
terior to  fit  the  bore. 


FIG.  270. 

This  is  pushed  down 
the  bore  from  the  muzzle  until  it  rests  on  the 
bullet  jacket,  which  may  then  be  forced  out 
of  the  barrel. 

A  headless  Khell  extractor  consists  of  a  steel 
plug,  Fig.  271   of  the  general  shape  of  the 


FIG.  269, 


FIG.  271. 

inside  of  the  cartridge  case,  with  a  head  like 
that  of  the  cartridge.  A  steel  ball  rolls  freely 
in  a  groove  at  the  point,  the  groove  being 
inclined  outward  toward  the  point.  The 
extractor  is  roughened  on  the  side  opposite 
the  groove.  The  extractor  is  pushed  into  the 


SMALL  ARMS  AND  THEIR  AMMUNITION.  555 

headless  shell  by  the  bolt  of  the  gun,  the  gun  being  held  with 
the  muzzle  up.  The  muzzle  of  the  gun  is  then  pointed  down 
and  the  bolt  withdrawn,  extracting  the  extractor  and  the  headless 
shell. 

An  aiming  device  is  also  provided  for  purposes  of  instruction 
in  aiming.  It  consists  of  the  circular  steel  clip  a,  Fig.  272, 
which  embraces  the  gun  in  rear  of  the  rear  sight  and 
supports  the  standard  It  to  which  the  cage  c  may  be 
fixed  at  any  desired  height.  The  cage  contains  a  reflector 
so  arranged  that  the  instructor  sees  in  the  reflector  the 
images  of  the  gun  sights  and  of  the  object  aimed  at. 
He  may  therefore  correct  the  soldiers'  aim. 

A  cleaning  thong  and  brush  are  contained  in  a 
metal  case  carried  in  the  butt  of  the  stock.  The  case 
is  arranged  to  contain  also  a  quantity  of  oil  and  a 
metal  oil-dropper.  A  brass  cleaning  rod,  a  steel  front 
sight  cover,  and  a  suitable  screw  driver  are  provided 
with  each  piece. 

316.  Deviation.  Drift. — The  rifle  has  a  right-handed  twist. 
The  drift  proper  Is  therefore  to  the  right.  But  at  the  moment  that 
the  bullet  leaves  the  bore  the  muzzle  of  the  gun  is  actually  pointed 
to  the  left  of  its  aimed  position.  The  movement  of  the  muzzle  is 
probably  due  to  vibrations  of  the  ban-el  caused  by  the  passage  of 
the  bullet  through  the  bore.  The  barrel  being  held  firmly  at  the 
bands  the  vibrations  will  take  place  about  these  points  as  nodes. 
The  vibratory  movement  of  the  barrel  is  such  that  at  the  moment 
that  the  bullet  leaves  the  bore  the  muzzle  is  pointed  to  the  left 
of  its  aimed  position. 

The  horizontal  deviation  of  the  bullet  from  the  axial  plane  of 
sight  is  therefore  the  resultant  of  the  drift  clue  to  the  rifling  and 
the  deviation  due  to  the  vibration  of  the  barrel.  Following 
custom,  we  will  call  the  resultant  horizontal  deviation  the  drift. 

As  determined  by  experimental  firings  the  drift  of  the  220- 
grain  bullet,  fired  from  the  service  rifle,  is  to  the  left  of  the  axial 
plane  of  sight  up  to  a  range  of  850  yards,  and  beyond  that  range 
the  drift  is  to  the  right. 

In  order  to  minimize  the  deviation  at  the  most  important 
ranges  the  drift  slot  in  the  leaf  of  the  model  1905  sight  is  so  cut 


556  ORDNANCE  AND  GUNNERY, 

as  to  make  the  trajectory  cross  the  adjusted  line  of  sight  at  a  range 
of  1530  yards.  Within  that  range  the  drift  is  to  the  left  of  the 
line  of  sight,  its  maximum  value  being  1.8  inches  at  the  range  of 
1200  yards.  After  the  trajectory  crosses  the  line  of  sight  the 
drift  is  to  the  right  and  increases  rapidly  from  1.1  inches  at  1600 
yards  to  39.4  inches  at  2500  yards. 

VERTICAL  DEVIATION. — The  angles  of  elevation  of  the  rifle  as 
determined  from  actual  firings  at  different  ranges  are  all  greater 
than  the  computed  angles  of  elevation  for  the  ranges.  This  in- 
dicates that  at  the  moment  that  the  bullet  leaves  the  bore  the  posi- 
tion of  the  muzzle  due  to  the  vibratory  movement  of  the  barrel  is 
below  as  well  as  to  the  left  of  its  aimed  position.  The  difference 
between  the  observed  and  computed  elevations  hi  creases  with  the 
range,  as  it  should  since  the  effect  of  a  constant  difference  of  the 
angles  will  be  less  as  the  range  increases. 

The  .22-caliber  Gallery  Practice  Rifle. — The  gallery  practice 
rifle  differs  from  the  U.  S.  magazine  rifle,  model  1898,  known  as 
the  Krag-Jorgensen  rifle,  only  as  to  the  barrel  and  the  receiver. 
The  barrel  of  the  gallery  practice  rifle  is  a  .22-caliber  rifled  barrel 
adapted  to  fire  commercial  .22-caliber,  rim-fire,  short  or  long 
cartridges.  The  barrel  is  issued  assembled  with  a  suitable  ex- 
tractor to  a  modified  receiver.  Any  model  1898  rifle  may  be  con- 
verted into  a  gallery  practice  rifle  by  dismounting  the  .30-oaliber 
barrel  and  receiver  and  mounting  in  their  stead  the  .22-caliber 
barrel  and  receiver. 

"With  .22  caliber  long  cartridges,  a  range  of  50  feet  requires  the 
sight  to  be  set  at  100  yards,  and  a  range  of  100  feet  requires  a 
sight  setting  of  225  yards. 

AMMUNITION  FOR  THE  .30-CAL.  MAGAZINE  RIFLE. 

317.  The  Ball  Cartridge.— The  ball  cartridge,  Fig.  273,  con- 
sists of  the  cartridge  case,  the  primer,  the  charge  of  powder,  and 
the  bullet. 

THE  CARTRIDGE  CASE. — The  cartridge  case  is  made  from  a 
circular  disk  of  brass  cut  from  a  flat  ribbon  0.13  of  an  inch  thick. 
The  disk  is  first  bent  into  the  form  of  a  cup  and  then  drawn  out  in 
successive  operations  by  being  forced  by  punches  through  dies 


SMALL  ARMS  AND   THEIR   AMMUNITION.  557 

successively  diminishing  in  diameter.  In  each  draw  press  the 
length  of  the  cartridge  is  increased  and  its  diameters  and  thick- 
ness of  wall  diminished.  Six  draws  are  required  to  bring  the  car- 
tridge to  the  desired  size.  After  the  cupping  operation  and  after 


FIG.  273. 

each  of  the  first  four  draws  the  case  is  softened  by  annealing, 
which  removes  the  brittleness  of  the  metal  caused  by  the  drawing 
process.  The  cases  are  trimmed  as  required.  The  head  of  the 
cartridge  case  and  the  primer  pocket  are  formed  in  a  press.  The 
mouth  of  the  case  is  then  annealed  and  the  reduction  of  the  neck 
and  shoulder  is  accomplished  hi  three  operations  in  another  press. 
The  extractor  groove  is  turned  in  the  head,  and  the  vent  is  punched 
through  the  bottom  of  the  primer  pocket. 

BODY. — The  body  of  the  cartridge  is  of  greater  diameter  than 
the  rifled  bore  of  the  gun,  in  order  to  provide  the  necessary  chamber 
space  in  the  shortest  practicable  length.  The  enlarged  body  is  a 
disadvantage  in  that  it  increases  the  bulk  of  the  cartridge,  and 
requires  a  larger  chamber  in  the  gun  and  greater  thickness  in  the 
working  parts  of  the  gun.  But  in  the  present  development  of 
powders  it  has  not  yet  been  possible  to  produce  from  a  cylindrical 
cartridge  of  reasonable  length  the  desired  ballistics  for  the  rifle. 

HEAD  SPACE. — The  space  in  the  rifle  between  the  head  of  the 
bolt  and  the  surface  against  which  the  cartridge  bears  is  called 
the  head  space.  The  head  space  in  the  rifle  is  of  a  length  to  allow 
proper  clearance  between  the  bolt  and  the  head  of  the  cartridge 
•when  the  cartridge  is  fully  inserted  in  the  chamber.  The  head  of 
the  cartridge  should  always  occupy  the  same  position  in  the  rifle, 
in  order  that  the  blow  of  the  firing  pin  on  the  primer  may  be 
uniform,  thus  reducing  the  chances  of  misfires  and  punctured 
primers. 

In  order  that  the  position  of  the  primer  in  the  gun  shall  vary 
the  least  the  head  space  should  be  as  short  as  possible,  that  is,  the 
bearing  surface  of  the  cartridge  should  be  close  to  the  head  of  the 


558  ORDNANCE  AND  GUNNERY. 

cartridge,  since  in  the  manufacture  of  the  cartridge  the  variations 
in  a  short  dimension  are  likely  to  be  less  than  in  a  longer  one. 

The  cartridge  with  flanged  head,  Fig.  274,  used  in  former 
service  rifles,  has  an  advantage  over  the  present  cartridge  in  this- 
respect.  The  head  space  with  the  flanged  cartridge  measured  from 
the  seat  for  the  front  edge  of  the  flange,  was  about  TV  of  an  inch 


FIG.  274. 

long,  while  the  head  space  in  the  present  rifle  which  is  measured 
from  the  seat  for  the  sloping  shoulder  of  the  cartridge,  is  nearly 
two  inches  long.  In  addition  the  bearing  surface  of  the  present 
cartridge  is  sloped,  so  that  more  extensive  variations  in  the  posi- 
tion of  the  head  of  the  cartridge  are  likely  to  occur. 

THE  PRIMER. — The  primer,  Fig.  273,  consists  of  the  cup,  the 
anvil,  and  the  percussion  composition.  A  pellet  of  moist  percussion 
composition  is  put  into  the  cup  which  is  previously  shellacked 
so  that  the  composition  will  adhere.  A  shellacked  disk  of  paper  is 
pressed  in  tightly  over  the  composition  to  keep  out  moisture.  The 
anvil  of  hard  brass  is  then  forced  into  the  cup.  The  primers  are 
dried  for  several  days  in  a  dry  house. 

The  cup  of  the  primer  is  made  of  gilding  metal,  an  alloy  of 
copper  much  softer  than  the  brass  of  the  cartridge  case.  The 
metal  of  the  cup  must  be  sufficiently  soft,  and  of  the  proper  thick- 
ness, to  permit  a  large  part  of  the  blow  of  the  firing  pin  to  be 
transmitted  to  the  percussion  composition,  thus  insuring  explo- 
sion of  the  primer.  At  the  same  time  the  metal  must  be  suffi- 
ciently hard  to  resist  puncture  by  the  firing  pin.  The  firing  pin 
strikes  the  primer  with  an  energy  of  about  17  inch-pounds. 

The  priming  composition  is  as  follows: 

Chlorate  of  potash,  632  parts 
Sulphide  of  antimony,  320  parts 
Ground  glass,  212  parts 

Sulphur,  110  parts 


SMALL  ARMS  AND   THEIR  AMMUNITION'.  559 

The  finely  pulverized  ingredients  are  thoroughly  mixed  wet, 
and  the  composition  is  always  handled  wet,  in  which  condition  it 
is  safe  to  handle.  The  composition  is  called  the  H  48  composition. 

This  composition  is  safe,  sufficiently  sensitive,  and  emits  a 
large  bod}''  of  flame.  The  large  body  of  flame  makes  the  composi- 
tion superior  for  use  with  smokeless  powders  to  the  fulminate  of 
mercury  formerly  used  in  all  primers  and  still  largely  used  in  the 
primers  in  sporting  cartridges  and  others. 

The  primer  is  seated  slightly  below  the  head  of  the  cartridge  in 
order  to  diminish  the  liability  to  accidental  explosion  of  the  car- 
tridge in  handling. 

THE  POWDER  CHARGE. — The  powder  charge  consists  of  about 
51  grains  of  nitroglycerine  powder.  The  weight  of  powder  re- 
quired to  produce  the  muzzle  velocity  of  2800  feet  varies  in  dif- 
ferent lots  of  powder.  The  weight  of  charge  therefore  varies 
slightly  in  different  cartridges. 

318.  Bullets.— The  core  of  the  bullet,  Fig.  273,  is-  an  alloy  of 
16  parts  of  lead  and  one  part  of  tin.  The  jacket,  of  cupro-nickel, 
is  drawn  from  a  disk  in  the  same  manner  as  the  cartridge  case. 
The  lead  slug  is  forced  into  the  jacket,  the  point  of  the  bullet 
shaped  in  a  press,  and  the  rear  end  of  jacket  turned  squarely  over 
the  base  of  the  bullet. 

The  220-grain  bullet  is  shown  in  Fig.  275,  and  the  recently 
adopted  150-grain  bullet  in  Fig.  276.  The  220-grain  bullet  had  a 
muzzle  velocitj'  of  2200  feet,  the  maximum  x-v 
pressure  in  the  bore  of  the  rifle  being  about  /  A 

49,000  Ibs.     The  150-grain  bullet  is  given  a  /  \ 

muzzle  velocity  of  2800  feet  with  a  maximum 
pressure  of  45,600  pounds.  The  great  in- 
crease in  the  muzzle  velocity  makes  the 
trajectory  of  the  lighter  bullet  very  much 
flatter  than  that  of  the  220-grain  bullet,  and 


thus  correspondingly  increases  the  accuracy  • I0-  276* 

of  the  rifle.  It  might  be  expected  that  the  lighter  bullet  would 
suffer  greater  retardation  in  flight  from  the  resistance  of  the  air, 
but  this  bullet  with  its  sharp  point  encounters  less  resistance 
than  the  heavier  bullet  with  its  rounded  point.  Greater  accuracy 
at  all  ranges  therefore  results  from  the  lighter  bullet,  with  its 
higher  velocity  and  sharp  point. 


560 


ORDNANCE  AND  GUNNERY. 


The  bearing  surface  of  a  bullet,  that  part  of  the  bullet  that 
comes  in  contact  with  the  walls  of  the  bore,  should  end  abruptly, 
in  order  that  as  the  bullet  leaves  the  muzzle  the  bearing  against 
the  walls  of  the  bore  will  cease  at  the  same  instant  on  all  sides, 
and  the  .bullet  will  not  be  deflected  by  the  longer  contact  of  any 
one  point  with  the  walls  of  the  bore.  The  bearing  surface  of  the 
sen-ice  bullet  terminates  at  the  base.  The  base  of  the  bullet 
should  therefore  be  square  with  the  axis,  and  the  edge  of  the  base 
should  be  as  sharp  as  the  metal  of  the  jacket  will  permit. 

In  Fig.  277  is  shown  in  full  size  a  bullet  recently  tested.  The 
bullet,  of  copper,  weighed  175  grams.  The  bearing  surface  began 
about  f  of  an  inch  from  the  point  and  extended  to  about 
|  of  an  inch  from  the  base,  terminating  on  the  rear 
slope  of  the  bullet,  the  diameter  of  the  base  being  less 
than  the  caliber.  In  tests  for  comparative  accuracy  at 
500  yards  the  radius  of  the  circle  of  shots  was  4.2 
inches  for  the  150-grain  service  bullet,  5.6  inches  for 
the  220-grain  service  bullet,  and  25.6  inches  for  the 
experimental  copper  bullet.  On  examination  of  the 
copper  bullets,  recovered  after  firing,  the  marks  of  the 
rifling  were  found  extending  farther  to  the  rear  on  one 
side  of  the  bullet  than  on  the  others.  The  difference 
in  length  of  bearing  on  the  different  sides  is  sufficient  to  account 
for  the  inaccuracy. 

319.  The  Blank  Cartridge. — The  bullet  of  the  ball  cartridge 
guides  the  cartridge  from  the  magazine  into  the  chamber  of  the 
rifle.  In  order  that  blank  cartridges  may  be  loaded  from  the 
magazine,  a  hollow  paper  bullet,  Fig.  278,  replaces  the  metal  bullet 


FIG.  277. 


FIG.  278. 


of  the  ball  cartridge.  The  paper  bullet  is  charged  with  5  grains 
of  E.  C.  powder  held  in  place  by  a  drop  of  shellac.  The  bullet  is 
made  by  rolling  a  strip  of  paper  into  a  tube  of  proper  length,  the 
end  of  the  tube  being  afterwards  closed  into  the  rounded  head 


SMALL  ARMS  AND  THEIR  AMMUNITION. 


561 


by  pressure  in  a  machine.  The  strip  of  paper  that  forms  the  tube 
is  gummed  only  on  the  outside  edge  so  that  the  charge  may  readily 
burst  the  bullet  at  the  muzzle  of  the  gun.  If  the  paper  were 
gummed  over  its  entire  length  the  bullet  would  be  so  stiff  that  it 
might  act  as  a  rocket  and  do  injury  at  some  distance  from  the 
muzzle. 

The  propelling  charge  in  the  cartridge  case  is  10  grains  of  E.  C. 
powder. 

The  blank  cartridge  is  made  TV  of  an  inch  shorter  than  the  ball 
cartridge,  to  prevent  the  accidental  assembling  of  a  ball  cartridge 
into  a  clip  with  blank  cartridges.  The  machine  in  which  this 
operation  is  performed  is  adapted  for  cartridges  of  one  length  only. 

The  Dummy  Cartridge. — In  order  that  the  dummy  cartridge, 
Pig.  279,  may  be  readily  distinguished  from  the  ball  cartridge  both. 


FIG.  279. 

by  sight  and  touch,  the  case  of  the  dummy  cartridge  is  tinned  and 
corrugated,  and  three  holes  are  bored  through  the  bottoms  of  the 
corrugations.  These  are  means  intended  to  diminish  the  chances 
of  the  insertion  of  a  ball  cartridge  in  the  rifle  when  drilling  with 
dummy  cartridges. 

The  Guard  Cartridge. — The  long  range  of  the  bullet  of  the 
ball  cartridge  and  its  great  penetrative  power  render  the  ball 
cartridge  unsuitable  for  the  use  of  guards  in  times  of  peace,  and 
for  use  in  cities  or  other  crowded  places  at  times  of  riot  and  dis- 


FIG.  280. 


turbance.  The  guard  cartridge,  Fig.  280,  is  provided  for  these 
uses.  The  unjacketed  lead  bullet  weighs  117  grabs  and  is  given 
a  velocity  of  1150  feet.  The  cartridge  gives  good  results  at  100 
yards  and  has  sufficient  accuracy  for  use  at  150  and  200  yards. 


562 


ORDNANCE  AND  GUNNERY. 


The  lead  bullet  is  deformed  on  striking  and  has  little  pene- 
trative power,  so  that  it  is  not  likely  to  cause  injury  at  a  distance 
to  innocent  persons. 

320.  Proof  of  Ammunition. — Ammunition  is  proved  by 
velocity  and  accuracy  tests  made  with  the  arm  in  which  the 
ammunition  is  to  be  used.  Service  rifle  cartridges  are  also  tested 
to  determine  whether  they  are  waterproof. 

VELOCITY  TEST. — The  velocity  is  measured  at  53  feet  from  the 
muzzle,  the  first  velocity  screen  being  placed  3  feet  from  the 
muzzle  and  the  two  screens  100  feet  apart.  The  mean  velocity  of 
10  shots  must  not  differ  more  than  15  feet  from  the  standard. 

ACCURACY  TEST. — The  accuracy  test  for  rifle  ammunition  con- 
sists of  several  series  of  10  shots  each  fired  at  a  target  500  yards 
from  the  muzzle.  The  gun  is  fixed  in  a  rest.  The  target  is  a 
heavy  steel  plate  about  20  feet  square,  painted  white  and  marked 
with  horizontal  and  vertical  black  lines  2  feet  apart. 

The  horizontal  and  vertical  coordinates  of  each  shot  mark  are 
measured  from  a  convenient  origin.  The  means  of  the  horizontal 
and  vertical  coordinates  are  respectively  the  horizontal  and  ver- 
tical coord  mates  of  the  center  of  impact. 

The  distance  of  each  shot  from  the  center  of  impact  is  measured 
and  the  mean  of  these  distances  is  the  mean  radius  of  the  group  of 
shots,  or,  as  it  is  sometimes  called,  the  radius  of  the  circle  of  shots. 

The  mean  of  the  vertical  distances  of  the  shots  from  the  center 
of  impact  is  the  mean  vertical  deviation,  and  the  mean  of  the  hori- 
zontal distances  from  the  center  of  impact  is  the  mean  horizontal 
deviation. 

In  the  proof  of  ammunition  the  mean  horizontal  deviation  is 
not  measured,  as  the  horizontal  deviation  depends  upon  the 
atmospheric  conditions  rather  than  upon  the  ammunition. 

The  results  of  recent  comparative  tests  of  the  220-grain  and  150- 
grain  bullets  in  the  service  rifle  are  shown  in  the  following  table. 


Bullet. 

Charge, 
Grains. 

Pres- 
sure, 
Lbs. 

Velocity,  f.  s. 

Accuracy 
500  Yards. 

Pene- 
tration 
500 
Yards, 
Inches. 

Muzzle. 

1000 
Yards. 

Had. 

M.V.D. 

220-grain    1903    

44 
51 

49000 
45000 

2200 
2730 

980 
1130 

5.6 
4.2 

4.2 

2.5 

23.3 
32.5 

ISO-grain    1906    

SMALL  ARMS  AND   THEIR  AMMUNITION.  563 

Equipment  for  Accuracy  Test. — As  it  would  often  be  most  in- 
convenient to  make  on  the  target  the  measurements  necessary  for 
the  determination  of  the  mean  radius  arid  deviations  of  a  group  of 
shots,  the  ammunition  proof  range  is  provided  with  a  camera 
obscura  in  a  building  in  front  and  to  one  side  of  the  target  and  near 
it.  The  lens  of  the  camera  forms  an  image  of  the  target  on  a 
paper  facsimile  of  the  target  constructed  to  the  proper  scale  so 
that  the  lines  of  the  image  coincide  with  the  lines  of  the  target 
facsimile.  An  observer  in  the  camera  marks  with  a  pencil  the 
image  of  each  shot  mark  made  on  the  target,  and  the  desired 
measurements  are  then  conveniently  made  from  the  paper  fac- 
simile. 

WATERPROOF  TEST. — Cartridges  from  each  lot  manufactured 
are  immersed  in  water  at  a  depth  of  8  inches  for  a  period  of  24  or 
48  hours,  and  are  then  tested  for  velocity.  There  must  be  no  fall- 
ing off  in  velocity  due  to  the  entrance  of  moisture  into  the  case. 


CHAPTER  XVI. 

MACHINE   GUNS. 

321.  Service  Machine  Guns. — The  machine  guns  in  our  service 
are  the  Gatling  machine  gun  and  the  Maxim  automatic  machine 
gun.  The  guns  are  of  the  same  caliber  as  the  infantry  rifle  and 
use  the  same  ammunition. 

In  the  Gatling  machine  gun  the  operations  of  loading,  firing, 
and  extracting  the  empty  shell  are  effected  through  mechanisms 
actuated  by  a  crank.  The  crank  is  turned  by  the  gunner  at  a  rate 
to  produce  any  desired  rapidity  of  fire.  The  greatest  efficiency  is 
obtained  from  the  gun  at  a  rate  of  fire  of  600  rounds  per  minute. 
In  an  emergency  this  rate  can  be  greatly  increased. 

In  the  Maxim  automatic  machine  gun  the  operating  mechanism 
is  actuated  by  the  recoil,  so  that  after  the  first  shot  is  fired  the 
firing  continues  without  effort  on  the  part  of  the  gunner  as  long 
as  the  trigger  is  pressed.  The  rate  of  fire  from  the  gun  depends 
upon  the  condition  of  the  barrel  and  mechanism.  In  a  new  gun 
250  cartridges  in  a  single  belt  are  fired  at  the  rate  of  650  shots  a 
minute.  After  8000  rounds  this  rate  is  reduced-  to  about  325 
shots  a  minute.  In  the  continuous  firing  of  1000  rounds  the  rate 
of  fire  from  a  new  gun  is  about  400  rounds  a  minute. 

The  Gatling  gun  has  the  advantages  of  a  more  rapid  rate  of 
continuous  fire,  and  of  a  complete  control  of  the  rate  of  fire  at  all 
times.  The  fire  of  the  automatic  gun  is  however  sufficiently  rapid, 
the  aiming  is  not  interfered  with  by  the  operation  of  a  crank,  and 
the  gun  is  lighter  and  more  readily  transported.  It  has  therefore 
been  adopted  as  the  principal  machine  gun  for  our  service. 

Machine  gun  fire  has  recently  become  of  such  importance. in 

564 


SMALL  ARMS  AND   THEIR  AMMUNITION. 


565 


battle  that  a  machine  gun  platoon,  armed  with  two  automatic 
machine  guns,  is  organized  in  each  battalion  of  infantry  and  in 
each  squadron  of  cavalry,  so  that  six  machine  guns  now  accom- 
pany each  regiment  into  the  field. 

The  Gatling  Machine  Gun.—  Fixed  to  a  central  shaft  8,  Fig. 
281,  are  the  ten  .30-caliber  rifled  barrels  B  held  in  the  barre! 


FIG.  281. 

plates  P;  the  carrier  block  C,  provided  with  grooves  which  re- 
ceive the  cartridges  successively  and  guide  them  into  the  barrels, 
the  lock  cylinder  L,  provided  with  guide  slots  hi  which  the  breech 
blocks  for  the  barrels  slide  to  close  and  open  the  breech;  and  the 
worm  wheel  G,  by  means  of  which  the  shaft  and  attached  parts 
are  rotated.  The  shaft  is  supported  at  each  end  in  a  frame,  the 
sides  of  which  also  support  the  shaft  of  the  rotating  crank  K. 

The  parts  behind  the  rear  barrel  plate  are  completely  inclosed 
in  a  cylindrical  bronze  casing  which  keeps  out  dust  and  protects 
the  operating  parts  against  injury.  Within  the  casing  is  a  hollow 
cylinder,  called  the  cam  cylinder,  on  the  interior  surface  of  which 
a  continuous  cam  groove  is  cut. 

The  breech  bolt,  Fig.  282,  one  for  each  barrel,  carries  the  firing 


FIG.  282. 


pin  a,  and  its  spring,  and  the  extractor  d.  The  guide  rib  e  at 
the  bottom  of  the  bolt  engages  in  a  guide  slot  of  the  lock  cylinder, 
L  Fig.  281.  The  lug  c  on  top  of  the  bolt  engages  in  the  cam 
groove  cut  in  the  walls  of  the  cam  cylinder. 


566 


ORDNANCE  AND  GUNNERY. 


The  cam  groove,  represented  in  Fig.  283  as  though  visible 
through  the  casing  and  cam  cylinder,  extends  continuously  around 
the  interior  of  the  cylinder.  The  top  and 
bottom  parts  of  the  groove,  a  and  6,  follow 
lines  cut  from  the  cylinder  by  planes  at  right 
angles  to  its  axis.  These  parts  of  the  groove 
are  joined  by  the  inclined  parts  cd.  The  cam 
cylinder  is  fixed  to  the  casing  and  does  not 
revolve. 

322.  OPERATION. — As  the  lock  cylinder,  L  Fig.  281,  rotates 
with  the  barrels  in  a  clockwise  direction,  the  uppermost  breech 
bolt  is  in  its  rearmost  position,  being  held  there  by  the  lug  c  of  the 
bolt  moving  in  the  circular  part  a  of  the  groove.  While  the  bolt 
is  in  this  position  a  cartridge  is  placed  by  the  feed  mechanism  in 
the  top  groove  of  the  lock  cylinder  C  in  front  of  the  bolt.  As 
the  bolt  in  its  rotation  moves  downward  on  the  right  side  it  is 


Fio.  283. 


5 


FIG.  284. 


moved  forward  by  the  cam  groove  cd  and  pushes  the  cartridge 
into  the  barrel.  During  this  movement  the  cocking  head  of  the 
firing  pin,  b  Fig.  282,  is  caught  by  a  grooved  rib,  R  Figs.  283  and 
284,  and  the  firing  pin  is  prevented  from  moving  forward  with  the 
bolt.  The  method  of  operation  will  be  understood  from  Fig.  284, 
which  shows  a  development  of  the  cam  groove  and  rotating  parts. 
The  lines  dd  and  cc  in  Fig.  284  represent  respectively  the  develop- 
ments of  the  parts  a  and  b  of  the  groove  as  shown  in  Fig.  283. 


MACHINE  GUNS. 


567 


-—a 


When  the  barrel  is  in  its  lowest  position  the  head  of  the  firing 
pin  leaves  the  rib  R,  and  the  firing  pin,  under  the  action  of  its 
spring,  strikes  and  fires  the  cartridge.  As  the  breech  bolt  moves 
upward  on  the  left  side  it  is  drawn  to  the 
rear  by  the  cam  groove,  extracting  the  fired 
shell  from  the  barrel  and  ejecting  it  to 
the  left  through  a  slot  in  the  casing. 

THE  FEED. — A  hopper  is  formed  in  the 
top  of  the  bronze  casing  immediately  over 
the  carrier  block,  C  Fig.  281  and  e  Fig.  285. 
The  device,  called  the  Bruce  feed,  for 
feeding  cartridges  to  the  gun,  is  fixed  in 
a  socket  at  the  mouth  of  the  hopper. 
Pivoted  on  the  standard,  ac  Fig.  285,  is 
a  swinging  piece  6,  provided  with  two 
flanged  grooves  which  engage  the  heads  of 
the  cartridges:  by  the  flange  of  the  1898 
cartridge,  and  by  the  groove  of  the  1903 
cartridge.  The  grooves  in  6  are  quickly 
filled  by  stripping  the  cartridges  from  the 
paper  boxes  in  which  they  are  packed. 
The  cartridges  from  one  of  the  grooves  in 
6  pass  immediately  through  the  groove  in 
c  and  are  fed  one  at  a  time  to  the  carrier 
block  e  by  the  wheel  d  which  is  caused  to 
revolve  by  the  carrier  block.  When  one 
of  the  grooves  in  6  is  empty  the  weight 
of  the  cartridges  in  the  other  groove 
causes  the  piece  6  to  swing  to  one  side  and 
bring  the  full  groove  over  the  groove  hi  c. 

MOUNTS. — The  Gatling  gun  is  mounted, 
for  field  sendee,  on  a  shielded  wheeled  car- 
riage with  limber.  When  mounted  in  the 
casemates  of  permanent  or  temporary  fortifications  for  use  in 
repelling  landing  parties  and  in  protecting  the  land  approaches,  a 
fixed  mount  is  provided. 

Blank  Cartridge  for  Gatling  Gun. — When  the  blank  cartridge 
for  the  infantry  rifle  is  used  in  the  Gatling  gun  the  blunt  end  of 


FIG.  285. 


568 


ORDNANCE  AND  GUNNERY. 


C 


a 
I 


o 
co 

<M 


MACHINE  GUNS. 


569 


the  paper  bullet  often  catches  on  a  shoulder  at  the  rear  end  of  the 
barrel,  thus  preventing  insertion  of  the  cartridge  and  causing  the 
mechanism  to  jam. 

A  special  blank  cartridge  is  therefore 
made  for  the  gun.  The  cartridge  case 
is  extended  to  the  length  of  the  com- 
plete ball  cartridge  and,  after  the  inser- 
tion of  the  powder  charge,  the  mouth 
of  the  case  is  closed  into  the  rounded 
form  of  the  point  of  the  220- grain  bullet. 

323.  The  Maxim  Automatic  Machine 
Gun. — The  Maxim  automatic  machine 
gun  has  a  single  barrel,  arid  the  recoil 
of  the  barrel  and  attached  mechanism  is 
utilized  to  perform  the  operations  neces- 
sary in  continuous  firing. 

The  barrel,  32  Fig.  286,  is  inclosed  in 
a  cylindrical  water  jacket  97,  and  slides 
in  its  bearings  in  stuffing  boxes  at  each 
end  of  the  water  jacket.  Fixed  to  the 
rear  end  of  the  water  jacket  is  the 
breech  casing  55,  a  rectangular  steel  box 
that  incloses  the  operating  mechanism 
and  provides  means,  35  and  54,  for  the 
attachment  of  the  gun  to  its  mount. 

METHOD  OF  ACTION. — The  barrel  and 
the  breech  mechanism  recoil  together 
until  after  the  bullet  has  left  the  bore. 
When  the  barrel  has  reached  the  end 
of  its  recoil  the  breech  mechanism 
continues  to  the  rear,  opens  the  breech, 
and  extracts  the  fired  shell;  and,  re- 
turning under  the  action  of  a  spring, 
inserts  a  new  cartridge  in  the  barrel  and 
fires  the  piece.  These  actions  are  re- 
peated as  long  as  the  trigger  is  pressed. 

The  cartridges  are  fed  to  the  gun  in  a  belt,  see  Fig.  291,  which 
is  automatically  drawn  through  the  feed  mechanism  above  the 


..Q. 


570 


ORDNANCE  AND  GUNNERY. 


breech  in  such  manner  as  to  present  a  new  cartridge  after  each 
discharge. 

RECOILING  PARTS. — The  recoiling  parts,  Fig.  287,  comprise  the 
barrel  a,  the  two  recoil  plates  6  fixed  to  the  breech  of  the  barrel, 
the  operating  crank  shaft  e  fixed  in  bearings  in  the  recoil  plates, 
and  the  breech  mechanism  which  slides  between  the  recoil  plates 
and  is  operated  by  means  of  the  crank  shaft  e. 

The  recoil  plates  slide  in  grooves  provided  in  the  sides  of  the 
breech  casing  55,  Fig.  286.  The  left  recoil  plate  extends  to  the 
front  of  the  breech  and  operates  the  feed  mechanism  above  the 
barrel.  The  crank  shaft  75  projects  on  both  sides  through  slots 
79  in  the  casing.  The  movement  of  the  recoiling  parts  to  the 


FIRING    POSITION. 


FIG.  288. 

rear  is  stopped  when  the  crank  shaft  strikes  the  rear  edges  of  the 
slots.  Fixed  to  the  right  end  of  the  shaft  is  the  cam  lever  57. 
During  the  recoil,  and  after  the  shot  has  left  the  bore,  the  lower 
surface  of  the  cam  lever  bears  on  the  roller  58,  and  as  the  recoil 
continues  the  cam  lever,  riding  on  the  roller,  is  rotated  upward, 
thus  producing  a  downward  movement  to  the  crank  on  the  shaft 
between  the  recoil  plates.  The  crank  is  seen  in  Fig.  287  and  at  i 
Figs.  288  and  289.  Attached  by  links  to  the  fusee,  g  Fig.  287, 
on  the  crank  shaft  outside  the  breech  casing,  is  the  operating 
spring  h  which  at  its  forward  end  is  attached  to  the  breech  casing. 
On  recoil  and  rotation  of  the  shaft  the  spring  is  extended,  and  at 
the  end  of  the  recoil  the  reaction  of  the  spring  returns  the  parts  to 
the  firing  position. 

324.  THE    BREECH    MECHANISM. — The    breech    mechanism   is 


MACHIXE  GUXS. 


571 


shown  in  Figs.  288  and  289.  It  consists  of  the  lock  k  which  con- 
tains the  firing  mechanism;  the  carrier  n,  a  narrow  piece  which 
slides  up  and  down  the  front  of  the  lock  and  is  provided  in  front 
with  a  flanged  groove  to  engage  the  head  of  the  cartridge;  and 
the  forked  link  /  pivoted  at  its  rear  end  to  the  crank  i  on  the 
operating  shaft  e.  The  breech  mechanism  slides  back  and  forth 
between  the  recoil  plates  6  in  grooves  cut  in  the  sides  of  the 
recoil  plates. 

The  parts  being  in  the  firing  position  the  flanged  groove  of  the 
carrier  n  engages  the  head  of  a  cartridge  in  the  feed  belt  above 
the  barrel  and  also  the  head  of  the  cartridge  in  the  barrel.  When 
the  piece  is  fired  the  barrel  and  breech  mechanism  start  to  the 


FIG.  289. 

rear  together.  At  the  end  of  the  movement  of  the  barrel,  the 
breech  mechanism  is  drawn  farther  to  the  rear  between  the  recoil 
plates  by  the  rotation  of  the  crank  i  as  shown  in  Fig.  289. 

In  this  movement  the  carrier  n  is  guided  by  its  bearings  q 
•which  move  on  the  upper  surfaces  of  solid  cams,  37  Fig.  286, 
fixed  to  the  side  plates  of  the  breech  casing.  The  movement  of 
the  carrier  is  at  first  straight  to  the  rear  withdrawing  the  cartridge 
from  the  belt  and  the  fired  shell  from  the  chamber.  The  carrier  is 
then  depressed  by  a  guide  lug,  43  Fig.  86  and  p  Figs.  288  and 
289,  attached  to  the  top  plate  of  the  breech  casing.  The  loaded 
cartridge  is  thus  brought  opposite  the  barrel  and  the  fired  shell 
opposite  the  ejector  tube  33.  The  reaction  of  the  coiled  spring 
now  returns  the  parts  to  the  firing  position,  the  carrier  n,  Figs. 
288  and  289,  moving  straight  to  the  front  in  its  depressed  position. 
After  the  cartridge  has  been  placed  in  the  chamber,  the  carrier  is 


572 


ORDNAXCE  AND  GUNNERY. 


slid  upward  by  the  action  of  the  finger  o  against  the  lifting  lever 
o',  the  finger  o  being  fixed  to  the  link  /.  The  carrier  leaves  the 
fired  shell  in  the  ejector  tube  where  it  is  held  by  a  spring  to  prevent 
its  falling  back  into  the  mechanism.  It  is  ejected  from  the  tube 
by  the  next  succeeding  shell. 

THE  FIRING  MECHANISM. — The  firing  mechanism,  shown  in  Fig. 
290,  is  contained  between  two  plates  k.  The  solid  part  of  the 
forked  link  j  acts  in  its  downward  movement  against  the  pro- 
jecting end  of  the  tumbler  c,  withdrawing  the  firing  pin  until  it  is 
caught  by  the  safety  catch  e.  At  the  same  time  the  sear  d  en- 


FIG.  290. 

gages  in  the  notch  of  the  tumbler  where  it  is  held  by  one  leaf  of  the 
spring  6.  The  trigger  h  is  placed  at  the  rear  outside  the  breech 
casing,  between  the  two  gun  handles.  A  forward  pressure  against 
its  upper  end  moves  the  trigger  bar  g  to  the  rear.  When  the 
trigger  is  pressed  the  lug  on  the  trigger  bar  that  engages  the  sear 
d  releases  the  sear  from  the  notch  in  the  tumbler  as  the  breech 
mechanism  moves  forward  in  closing,  and  holds  it  released  after 
the  breech  is  closed.  After  the  release  of  the  sear  the  firing  pin 
is  held  back  by  the  safety  catch  e.  The  link  j  in  the  last  part  of 
its  movement  upward  lifts  the  projecting  end  of  the  safety  catch 
and  releases  the  firing  pin,  which  under  the  action  of  the  spring 
6  flies  forward  and  fires  the  cartridge. 


MACHINE  GUNS.  573 

The  trigger  is  constantly  pressed  to  the  rear  by  the  spring  i 
and  is  provided  with  a  safety  catch  to  guard  against  accidental 
firing.  The  trigger  cannot  be  pressed  forward  for  filing  until 
the  safety  catch  is  lifted. 

325.  THE  WATER  JACKET. — In  continuous  firing  the  barrel  of 
an  automatic  rifle  becomes  very  highly  heated  and  if  not  cooled  in 
some  way  may  even  attain  a  red  heat.  The  walls  of  the  bore  are 
so  softened  by  the  heat  that  the  lands  of  the  rifling  are  soon  worn 
away  and  the  gun  loses  its  accuracy.  The  accuracy  is  completely 
destroyed  after  about  1000  rounds  fired  with  the  water  jacket 
empty.  The  necessity  of  cooling  the  barrel  during  firing  is  therefore 
apparent,  and  the  gun  should  never  be  fired,  except  in  emergency, 
without  water  in  the  jacket. 

The  water  jacket  of  the  Maxim  gun  holds  12  pints  of  water. 
The  barrel  of  the  gun  is  coated  with  copper  on  the  exterior  as  a 
protection  against  rust.  The  stuffing  boxes  through  which  the 
barrel  passes  are  packed  with  asbestos  packing. 

A  steam  tube,  89  Fig.  286,  is  fitted  in  the  upper  part  of  the 
water  jacket  to  provide  a  means  of  escape  for  the  steam  that  is 
formed  in  the  water  jacket  during  continuous  firing.  Near  each 
end  of  the  steam  tube  is  a  hole  89  for  the  admission  of  steam, 
and  at  the  front  end  a  hole  99  through  both  tube  and  water  jacket 
permits  escape  of  steam  to  the  exterior.  The  steam  tube  is  sur- 
rounded by  the  tubular  valve  96  which  slides  on  the  steam  tube 
and  closes  the  forward  or  rear  steam  port  according  as  the  gun  is 
depressed  or  elevated,  thus  preventing  the  entrance  of  water  into 
the  steam  tube  while  permitting  the  entrance  of  steam. 

THE  CARTRIDGE  BELT. — The  cartridge  belt,  Fig.  291,  is  formed 
of  two  pieces  of  flax  webbing  connected  by  brass  strips  and  eyelets 
between  adjacent  cartridges,  every  third  strip  projecting  about  an 
inch  beyond  the  bullet  edge  of  the  belt  to  guide  the  belt  properly 
through  the  feed  mechanism  of  the  gun.  A  flat  brass  handle  4 
inches  long  is  attached  to  each  end  of  the  belt. 

Each  belt  holds  250  cartridges. 

The  cartridges  are  quickly  and  evenly  inserted  into  the  belt 
pockets  by  means  of  a  small  belt-filling  machine,  Fig.  292,  which 
is  attached  to  a  bench  and  operated  by  hand. 

MOUNTS. — For  service  with  the  infantry  and  cavalry  the  auto- 


574  ORDNANCE  AND  GUNNERY. 

matic  gun  is  mounted  on  a  tripod,  Figs.  291  and  293.  It  is  trans- 
ported by  means  of  pack  animals.  For  transportation  the  legs  of 
the  tripod  fold  together  and  the  rear  leg  telescopes.  A  complete 
outfit  consists  of  five  packs.  The  gun  and  tripod  form  one  pack 
which  weighs,  with  the  equipment  of  the  animal,  275  pounds. 
Each  of  the  other  four  packs  consists  of  1500  rounds  of  ammuni- 
tion, and  accessories  for  the  gun  including  water  for  refilling  the 
water  jacket.  These  packs  weigh  complete  about  290  pounds 
each. 

The  gun  with  tripod,  and  water  jacket  filled  with  water,  weighs 
152  pounds.  It  may  therefore  be  readily  transported  by  hand 
over  short  distances  in  the  field.  The  legs  of  the  tripod  fully 
extended  to  the  front  and  rear  form  convenient  shafts  for  carrying. 

For  use  in  fortifications  the  gun  is  mounted  on  a  two-wheeled 
carriage  provided  with  shields.  The  parts  of  the  mount  connecting 
with  the  gun  are  alike  in  the  carriage  and  in  the  tripod  mount,  so 
that  the  guns  may  be  fitted  to  either  type  of  mount  as  desired. 

BLANK  FIRING  ATTACHMENT. — The  pressure  produced  in  the 
discharge  of  a  blank  cartridge  is  not  sufficient  to  operate  the 
mechanism  of  the  gun.  There  is  therefore  provided  for  use  in 
drill  with  blank  cartridges  an  attachment  called  the  drill  and 
blank  firing  attachment.  The  attachment,  Fig.  293,  is  affixed  to 
one  of  the  rear  gun  handles  and  acts,  through  the  continuous 
turning  of  a  crank  by  hand,  to  operate  the  crank  shaft  of  the 
recoil  mechanism  in  the  same  manner  as  when  operated  by  the 
explosion  of  a  ball  cartridge. 

326.  The  Maxim  One-pounder  Automatic  Gun. — This  gun, 
called  the  Pompom  from  the  noise  of  its  explosions,  is  constructed 
on  the  same  principles  as  the  .30-caliber  automatic  gun  above  de- 
scribed. 

On  account  of  the  greater  size  and  weight  of  the  parts  and  the 
increased  total  force  of  recoil,  an  additional  coiled  recoil  spring,  s 
Fig.  294,  surrounds  the  barrel  in  the  water  jacket.  The  spring,  as 
well  as  the  barrel,  is  coated  with  copper.  A  small  hydraulic 
cylinder  c  also  assists  in  checking  the  recoil.  The  cylinder  is 
held  in  the  rear  plate  of  the  breech  casing,  the  piston  p  of  the 
cylinder  being  connected  with  a  cross  bar  x  held  between  the 
rear  ends  of  the  recoil  plates. 


FIG.  292.— Belt  Filling  Machine. 


FIG.  293. — Attachment  for  Firing  Blank  Cartridges. 
MAXIM  .30-CALiBER  AUTOMATIC  MACHINE  GUN. 


MACHINE  GUNS.  575 

The  caliber  of  the  gun  is  1.457  inches.  It  fires  a  shell  weighing 
one  pound,  with  a  bursting  charge  of  4/10  of  a  pound. 

The  Colt  Automatic  Machine  Gun. — The  operation  of  the  Colt 
automatic  machine  gun,  Fig.  295,  is  effected  through  the  direct 
action  of  the  powder  gases  on  the  end  of  a  swinging  lever  I.  A 
vent  is  cut  through  the  bottom  of  the  stationary  barrel  a  short 
distance  in  rear  of  the  muzzle.  When  the  bullet  has  passed  the 
vent  a  portion  of  the  powder  gases  enter  the  vent  and  impinge  on 
a  piston  p  attached  to  the  lever  I.  The  blow  on  the  piston  causes 
the  lever  to  revolve  downward  and  to  the  rear  against  the  action 
of  a  coiled  spring  s  which  at  the  end  of  the  movement  returns  the 
lever  to  its  former  position. 

The  movement  of  the  lever  is  communicated  by  the  connecting 
bar  c  to  the  mechanisms  in  the  rear,  and  actuates  these  mechan- 
isms to  perform  the  successive  operations  necessary  for  the  main- 
tenance of  continuous  fire. 

The  cartridges  are  fed  to  the  gun  in  a  belt  similar  to  that 
described  for  the  Maxim  gun.  The  feeding  of  the  belt  is  accom- 
plished by  the  feed  wheel  w  under  the  rear  end  of  the  barrel. 


CHAPTER  XVII. 

SUBMARINE  MINES  AND  TORPEDOES.  SUBMARINE 
TORPEDO  BOATS. 

327.  Submarine  Mines  and  Torpedoes. — A  submarine  mine  is 
a  charge  of  explosive  confined  in  a  strong  case  anchored  in  posi- 
tion under  the  surface  of  the  water. 

A  torpedo  is  a  submarine  vehicle  charged  with  explosive.  The 
term  torpedo  formerly  included  fixed  as  well  as  moving  mines, 
and  still  includes,  to  a  certain  extent,  both  these  classes. 

History. — The  first  recorded  experiments  with  submarine 
mines  were  made  by  David  Bushnell  of  Connecticut,  in  1775. 
His  mines  contained  charges  of  black  powder,  and  explosion  was 
effected  by  means  of  clockwork,  which,  after  being  set  in  motion, 
allowed  sufficient  time  before  the  explosion  for  the  operator  to  get 
clear. 

Bushnell  also  constructed  a  submarine  boat  for  the  purpose  of 
conveying  his  mines  to  hostile  vessels.  The  boat,  Fig.  296,  was 
formed  of  two  sides,  each  shaped  like  the  upper  shell  of  a  tortoise. 
Entrance  was  gained  through  a  hatch  in  the  top.  It  carried  but 
one  operator,  who  moved  the  craft  by  means  of  screw  propellers. 
The  explosive  was  carried  hi  a  case  with  the  firing  mechanism,  on 
the  back  of  the  boat,  and  was  fastened  by  a  rope  to  the  stem  of  a 
wood  screw  which  projected  through  the  top  of  the  boat.  The 
operator  was  expected  to  bring  the  craft  under  the  hostile  ship, 
and  fasten  the  wood  screw  in  the  ship's  wooden  bottom.  This 
effected,  the  moving  away  of  the  submarine  boat  would  release 
the  mine  and  set  the  clockwork  in  motion,  to  explode  the  charge 
after  a  sufficient  interval  of  time. 

576 


SUBMARINE  MINES  AND  TORPEDOES. 


577 


An  attempt  was  actually  made  in  1776  with  this  boat  against 
the  English  man-of-war  Eagle  in  the  harbor  of  New  York.  The 
operator  claimed  that  he  found  the  vessel,  and  that  in  attempting 
to  fasten  the  screw  in  her  bottom  he  struck  iron.  In  looking  for 
a  better  location  he  lost  the  vessel.  He  released  the  magazine  in 
the  harbor,  and  an  hour  afterward  the  explosion  occurred. 

Bushnell  also  attacke'd  the  English  fleet,  at  Philadelphia  in 
1777,  with  drifting  torpedoes.'  This  attempt  was  also  unsuccessful. 


FIG.  296. 


Robert  Fulton  experimented  with  torpedoes  from  1797  to  1810. 
In  1801  he  succeeded  in  sinking  the  first  vessel,  a  small  one,  with  a 
submarine  mine.  The  mine  contained  20  pounds  of  gunpowder. 
In  1804  he  conducted,  for  the  English,  an  unsuccessful  attack  with 
mines  against  the  French  fleet  in  the  harbor  of  Boulogne.  The 
mines  exploded  but  did  no  harm  to  the  French  ships. 

In  1842  Samiiel  Colt  applied  electricity  to  the  firing  of  sub- 
marine mines,  and  in  the  following  years  was  successful  in  numer- 
ous experiments  in  the  explosion  of  mines  at  great  distances  from 
the  operator. 

Mines  and  torpedoes  were  first  successfully  used  in  war  by  the 
Confederates  in  our  Civil  War.  With  imperfect  appliances  they 


578 


ORDNANCE  AND  GUNNERY. 


succeeded  in  sinking  or  seriously  damaging  more  than  thirty 
United  States  ships.  Their  success  attracted  the  attention  of  the 
world  to  this  method  of  naval  attack  and  defense,  with  the  result 
that  there  has  followed  great  improvement  in  the  appliances  and 
methods  employed,  and  the  means  for  submarine  warfare  are  now 
given  eaniest  consideration  by  all  maritime  nations. 

328.  Confederate  Mines. — The  mines  used  by  the  Confederates 
were  of  various  forms.  The  simplest  and  one  of  the  most  effective 
mines  was  made  of  a  barrel,  which  was  partially  filled  with  black 
gunpowder.  The  charge  was  usually  about  100  pounds.  The 
barrel,  Fig.  297,  was  provided  with  pointed  ends  to  prevent  its 
being  overturned  by  the  current.  It  was  moored  to  float  5  or  6 


FIG.  297. 

feet  below  the  surface  of  the  water,  and  a  depending  weight  kept 
the  top  of  the  barrel  uppermost.  Screwed  into  sockets  on  top  of 
the  barrel  were  a  number  of  percussion  or  chemical  fuses.  A 
vessel  striking  one  of  these  would  explode  the  mine. 

The  chemical  fuse  consisted  of  a  small  glass  tube  filled  with 
sulphuric  acid  and  surrounded  by  a  mixture  of  chlorate  of  potash 
and  white  sugar,  the  whole  enclosed  hi  an  outer  lead  tube.  The 
lead  tube  was  crushed  by  the  blow  of  a  striking  vessel  and  the 
glass  tube  broken.  The  action  of  the  sulphuric  acid  on  the  mixture 
of  chlorate  of  potash  and  white  sugar  produced  fire,  which  was 
communicated  to  the  powder  charge  of  the  mine  by  a  priming  of 
black  powder. 

Another  very  effective  buoyant  mine,  known  as  the  Singer 
mine,  is  shown  in  Fig.  298.  The  case,  made  of  tin,  was  of  size 
sufficient  to  hold  from  50  to  100  pounds  of  gunpowder,  and  to 
provide  sufficient  air  space  a  for  flotation.  A  percussion  cap  was 
held  in  a  cup  hi  the  lug  e  in  the  midst  of  the  powder  charge,  and 


SUBMARINE  MINES  AND   TORPEDOES. 


579 


the  upper  end  of  the  rod  d  was  close  to  the  cap.  A  firing  bolt  6 
was  held  back  against  the  pressure  of  a  spiral  spring  by  the  pin  g. 
A  heavy  iron  cap  c,  connected  by  a  wire  to 
the  pin,  rested  on  the  top  of  the  mine.  When 
the  mine  was  struck  the  cap  was  knocked  off. 
The  cap  in  falling  pulled  out  the  pin  g.  The 
firing  mechanism  would  then  act  and  explode 
the  mine. 

In  shallow  waters,  frame  and  spar,  or  pile, 
torpedoes  were  used.  The  frame  torpedo, 
Fig.  299,  consisted  of  a  number  of  inclined 
timbers  framed  together  and  supporting  at 
their  upper  ends  explosive  shell  provided 
with  percussion  caps. 

Two  forms  of  the  spar  torpedo  are  shown 
in  Figs.  300  and  301.  The  spar  torpedo  was 
also  used  for  offensive  operations  in  boats. 
The  spar,  with  torpedo  at  the  end,  was 
carried  projecting  from  the  bow  of  a  launch. 

The  most  noteworthy  exploit  with  a  spar  torpedo  was  that  of 
Lieut.  W.  B.  Gushing,  U.  S.  Navy,  who  in  1864  attacked  in  a 
launch  the  Confederate  ironclad  Albemarle  which  was  tied  to  a 
dock  in  the  river  at  Plymouth,  N.  C.  The  Albemarle  was  sunk  by 


FIG.  298. 


the  explosion  of  the  torpedo.     So  was  the  launch.    Lieutenant 
Gushing  and  one  member  of  his  crew  of  thirteen  escaped. 

The  Confederates   also    made  use  of  submarine  boats  carrying 
torpedoes,   and    they    sunk   by   these    means  the  United  States 


580 


ORDNANCE  AND  GUNNERY. 


frigate   Housatonic  in  Charleston  Harbor  in  1864.    The  submarine 
boat  used  on  this  occasion  was  worked  by  a  crew  of  nine  men  who 


FIG.  300. 

operated  the  propellers  by  hand.    The  boat  and  her  crew  were 
carried  down  with  the  Housatonic. 

Spanish  Mechanical  Mine. — Fig. 
302  represents  a  Bustamente  contact 
mine.  Seventeen  of  these  mines  were 
removed  by  our  Navy  from  the  harbor 
of  Guantanamo,  Cuba,  after  the  cap- 
ture of  the  harbor  in  1898. 

The  mine  is  circular  in  cross  sec- 
tion. It  carried  a  charge  of  100 
pounds  of  wet  guncotton  hi  the 
cylinder  a  and  a  priming  charge  of 
dry  guncotton  in  the  chamber  6. 
Against  the  chemical  fuse  c,  a  bottle 
containing  sulphuric  acid  and  sur- 
rounded by  a  mixture  of  chlorate  of 
potash  and  sugar,  rest  the  ends  of 
six  iron  rods  or  plungers  d  whose 
outer  ends  are  connected  to  the  six 
pivoted  contact  arms  e.  A  blow  on  any  one  of  the  arms  e  would 
cause  a  plunger  to  break  the  fuse.  Ignition  of  the  priming  charge 
and  explosion  of  the  bursting  charge  would  follow. 


SUBMARINE  MINES  AND   TORPEDOES. 


581 


329.  Electric  Mines. — Mechanical  mines  such  as  those  de- 
scribed above,  when  once  planted,  render  the  waterways  dangerous 
to  friend  and  foe  alike.  This  great  disadvantage  is  overcome  in 
modern  practice  by  the  use  of  electrically  controlled  mines  which 
may  be  made  instantly  operative  or  harmless  at  the  will  of  an 
operator  on  shore. 


SINGLE  CONDUCTOR  CABLES 1~~ 

—  — ™       MULTlPLt  CABU 
-RAISING  ROPE 


FIG.  303. 


BUOYANT  MINES. — A  modern  buoyant  mine  is  shown  in  Fig. 
303.  The  spherical  case  of  steel  contains  the  explosive  and  the 
circuit-closing  and  firing  devices,  with  sufficient  air  space  for 
flotation.  A  continuous  insulated  cable  extends  from  the  mining 
casemate  in  the  fortification  to  the  mine  in  position.  The  firing 
circuit  is  broken  at  the  mine,  and  the  electrical  arrangements  are 
such  that  the  mine  may  be  fired  by  the  operation  of  the  circuit- 
closer  when  the  mine  is  struck  by  a  vessel,  or  at  any  time  at  the 
will  of  the  operator  in  the  mining  casemate.  Or  the  striking  of  a 


582  ORDNANCE  AND  GUNNERY. 

mine  may  be  automatically  signaled  to  the  operator,  who  may 
then  fire  it  at  once,  or  after  a  few  moments  delay,  in  order  to  allow 
a  ship  to  get  well  over  it,  or  not  fire  it  at  all. 

Buoyant  mines  are  moored  at  a  submergence  of  about  5  feet 
at  low  water,  so  that  they  may  be  near  enough  to  the  surface  to  be 
struck  by  passing  vessels  and  yet  not  near  enough  to  be  readily 
seen.  They  are  not  in  general  used  in  water  less  than  20  feet 
deep.  They  may  be  operated  successfully  in  water  150  feet  deep. 
In  order  to  obtain  the  necessary  buoyancy  the  mines  used  in 
waters  of  the  greatest  depths  are  cylindrical  in  shape  with  hemi- 
spherical ends. 

GROUND  MINES. — Ground  mines  are  used  when  the  depth  of  the 
water  does  not  exceed  35  feet.  Th^y  rcct  cm  one  oottom.  A 
heavy  mushroom-shp.pcJ  case  contains  the  charge  of  explosive  and 
the  °hcLric  firing  device.  The  circuit- closing  device  is  carried  by 
a  buoyant  case  similar  in  shape  to  the  buoyant  mine.  The  buoy  is 
moored,  with  proper  submergence,  to  the  ground  mine.  When 
the  buoy  is  struck  by  a  passing  vessel  the  circuit-closer  within  it 
acts  in  precisely  the  same  manner  as  the  circuit-closer  in  the 
buoyant  mine,  and,  if  desired,  completes  the  firing  circuit  that 
fires  the  charge  in  the  mine  resting  on  the  bottom. 

330.  The  Explosive. — Dynamite  and  guncotton  are  the  prin- 
cipal explosives  used  in  submarine  warfare. 

Dynamite  has  been  used  in  the  mines  of  the  United  States 
service/  It  has  the  advantages  of  cheapness  and  ease  of  ignition. 
Its  disadvantages  are  danger  in  handling,  liability  to  explosion 
when  a  derelict  mine  is  struck  by  a  vessel,  and  changing  sensibility 
to  the  action  of  the  detonator  when  freezing  and  uhawing.  If  the 
dynamite  becomes  wet,  through  a  leak  in  the  mine  case,  the  nitro- 
glycerine separates  from  the  absorbent. 

Guncotton  has  the  advantage  of  being  perfectly  safe  in  storage 
and  in  handling,  and  of  detonating  when  wet  if  a  small  amount 
of  dry  guncotton  be  present.  The  dry  cotton  must  be  in  close 
contact  with  the  wet.  Too  much  water  will  make  the  detonation 
uncertain.  The  explosive  force  of  guncotton  is  less  than  that  of 
dynamite. 

Excellent  results  have  recently  been  obtained  in  submarine 
work  with  the  explosive  tri-nitro-toluol. 


SUBMARINE  MINES  AND  TORPEDOES.  583 

The  Charge.— Charges  varying  from  100  to  1000  pounds  of  ex- 
plosive have  been  used  in  mines.  A  charge  of  100  pounds  ex- 
piocied  In  cGii'uaCw  Trltli  «  warship'?  bottom  will  disable  and  prob- 
ably sink  the  ship. 

In  recent  experiments  with  a  submerged  target  built  in  exact 
representation  of  the  bottom  of  a  battleship,  the  explosion  of  a 
12-inch  mortar  shell  containing  63  pounds  of  high  explosive,  at  a 
distance  of  20  feet  from  the  target  and  at  a  depth  of  15  feet, 
produced  serious  injury  to  the  target;  64  pounds  at  a  distance  of 
15  feet  nearly  disrupted  the  target  and  caused  bad  leakage,  pro- 
ducing dangerous  injury;  while  130  pounds  at  a  distance  of  15 
feet  disrupted  the  double  bottom  and  caused  the  target  to  sink 
immediately.  The  results  showed  the  utility  of  this  method  of 
attack  on  vessels,  and  the  desirability  of  using  as  large  an  explo- 
sive charge  as  possible  in  the  projectiles  for  the  seacoast  mortars. 

General  Henry  L.  Abbott,  Corps  of  Engineers,  U.  S.  Army, 
conducted  a  very  extensive  series  of  subaqueous  experiments  with 
different  explosives.  He  deduced  the  following  formulas  for  the 
energy  an.d  pressure  delivered  at  a  distance  by  a  subaqueous  ex- 
plosion. 

58C 


W= 


(D  +  0.01)2'1 


1,832,000(7  Y 

:i>+o.oi)2-v 


in  which  W  represents  the  energy  per  square  inch, 
P  the  pressure  in  pounds  per  square  inch, 
C  the  weight  of  charge,  in  pounds, 
D  the  distance  in  feet. 

Applying  the  pressure  formula  to  the  explosions  of  the  three 
mortar  shell  in  the  vicinity  of  the  battleship  target,  we  find  that 
the  pressures  on  the  target  were,  in  order,  3574,  5401,  and  8662 
pounds  per  square  inch. 

331.  Defensive  Mine  Systems. — The  submarine  mine  system 
is  used  as  an  auxiliary  in  the  defense  of  a  river  or  harbor  in 
connection  with  the  land  fortifications,  and  its  chief  purpose  is 
to  so  limit  and  obstruct  the  approach  of  the  enemy's  vessels  that 


584 


ORDNANCE  AND  GUNNERY. 


they  will  be  compelled  to  make  frontal  attack  on  the  fortifications 
and  be  held  exposed  to  the  fire  of  the  heaviest  guns. 

In  order  that  the  most  effective  fire  may  be  employed  the  outer 
lines  of  mines  are  planted  at  a  distance  from  the  fortifications,  not 
exceeding  the  most  effective  range  of  the  guns. 

The  usual  mine  system  for  the  defense  of  a  harbor  is  illustrated 
in  Fig.  304.  Concealed  and  protected  in  a  fortification  is  the 


FIG.  304. 

mining  casemate  C  which  contains  the  electric  generators,  bat- 
teries, and  instruments  needed  in  the  service  of  the  mines.  From 
this  point  the  mines  are  controlled. 

The  mines  are  planted,  in  the  waterways  to  be  defended,  in 
groups,  for  convenience  of  service. 

Multiple  conductor  cables,  one  for  each  group,  lead  from  the 
mining  casemate  to  junction  or  distribution  boxes  similar  to  that 


SUBMARINE  MINES  AND   TORPEDOES.  585 

shown  in  Fig.  303.  In  the  junction  box  the  conductors  of  the 
multiple  cable  are  separated  and  joined  to  the  conductors  of  single 
conductor  cables  which  lead  to  the  individual  mines  of  the  group. 
Thus  each  mine  has  its  own  cable  and  may  be  operated  inde- 
pendently of  all  the  other  mines. 

The  course  of  a  hostile  vessel  approaching  or  moving  through 
the  mine  fields  is  observed  by  means  of  the  range  and  position 
finding  system  of  the  fortification,  and  the  operator  in  the  mining 
casemate  is  apprised  of  the  proximity  of  the  vessel  to  any  mine. 

In  addition  to  the  groups  of  mines,  other  mines,  called  skirmish 
mines,  s  Fig.  304,  may  be  laid  on  single  cables  in  irregular  lines 
about  the  groups.  The  skirmish  mines  may  be  made  active  or 
safe  at  the  will  of  the  operator,  but  cannot,  on  account  of  their 
arrangement  on  a  single  cable,  be  fired  singly  by  judgment. 

The  arrangement  of  all  the  mines  is  such  that  a  vessel  can 
follow  no  reasonable  course  into  the  harbor  without  encountering 
several  mines.  Gaps,  left  between  the  groups  in  the  various  lines, 
form  a  more  or  less  tortuous  channel  which  allows  passage  to 
friendly  vessels.  Guide  boats  are  employed  to  conduct  friendly 
vessels  through  the  safe  passages. 

Subsidiary  waterways  not  of  service  to  the  defense  may  be 
closed  to  the  enemy  by  mechanical  mines,  which  contain  within 
themselves  the  electric  batteries  that  provide  the  firing  current. 

In  the  fortifications,  gun  batteries,  usually  of  3-inch  guns,  cover 
the  mine  fields,  and  protect  them  against  attempts  of  the  enemy 
to  clear  the  fields  by  countermining  from  boats. 

Search  lights  are  provided  to  illuminate  the  mine  fields  at 
night. 

332.  Countermining. — Countermining  consists  in  exploding 
and  cutting  adrift  the  fixed  mines  of  the  enemy  and  destroying 
their  cable  connections  by  the  explosion  of  other  mines  distributed 
among  them.  The  purpose  of  countermining  is  to  make  a  safe 
channel  through  the  mines  of  the  defense.  Countermining  is 
usually  done  at  night  from  small  boats. 

The  Removal  of  Mines. — The  experience  had  in  clearing  the 
harbors  of  the  United  States  of  mines  after  the  Spanish  War  in- 
dicates that  the  safest  way  to  remove  the  mines  is  to  explode  them 
in  place. 


586  ORDNANCE  AND  GUNNERY. 

Mobile  and  Automobile  Torpedoes. — The  mobile  torpedo  con- 
veys the  explosive  charge  under  the  water  and  explodes  the  charge 
against  the  bottom  of  the  enemy's  ship.  Mobile  torpedoes  ?.rc  ixO~w~ 
used  exclusively  by  navies,  and  all  sucV>  tcr^eaoes  are  self-propelling 
or  automobile.  The  nec^iuy  of  erecting  on  shore,  at  the  water's 
edge,  soeci?.!  giants  for  the  service  of  the  torpedoes,  and  the  necessity 
of  protecting  such  plants,  are  considerations  that  militate  against 
the  use  of  mobile  torpedoes  for  harbor  defense. 

The  Sims-Edison  Torpedo. — A  long  series  of  experiments  were 
made  a  number  of  years  ago  with  the  Sims-Edison  torpedo,  Fig. 
305,  to  determine  whether  this  torpedo  was  adapted  for  harbor 
defense. 

The  torpedo  consists  of  a  cylindrical  hull  with  conical  ends.  It 
is  28  feet  long,  21  inches  in  diameter,  and  is  supported  at  a  depth 


1 I 


iTEARING  GEAR. 


CABLE  TO  SHORE  STATION.— ^^ — , 
FIG.  305. 

of  5  feet  under  the  water  by  a  float,  to  which  it  is  connected  by  steel 
rods.  Two  balls  carried  above  the  float  enable  the  operator  on 
shore  to  observe  the  position  of  the  torpedo  and  to  direct  its  move- 
ment. The  torpedo  is  propelled,  steered,  and  exploded  by  elec- 
tricity. The  power  is  generated  at  a  station  on  shore  and  is  com- 
municated to  the  torpedo  through  a  cable  which  is  carried  coiled 
in  a  central  chamber  and  is  paid  out  as  the  torpedo  moves. 

A  charge  of  300  pounds  of  explosive  is  carried  in  the  head  of  the 
torpedo. 

The  results  obtained  in  the  experiments  were  not  sufficiently 
satisfactory  to  warrant  the  adoption  of  this  torpedo  for  the  harbor 
defense  service. 

333.  The  Whitehead  Torpedo. — The  Whitehead  torpedo,  Fig. 
306,  is  now  used  by  all  the  navies  of  the  world.  Its  motive  power 
is  furnished  by  compressed  air  which  is  stored,  at  a  pressure  of 
about  1100  pounds  per  square  inch,  in  a  tank  carried  by  the  torpedo. 


SUBMARINE  MINES  AND   TORPEDOES.  587 

The  torpedo  is  fired,  by  compressed  air  or  by  gunpowder,  from 
launching  tubes  that  are  mounted  on  the  ship's  deck  or  built  into 
the  ship  below  the  water  line.  A  torpedo  tube  arranged  for  firing 
with  compressed  air  is  shown  mounted  on  the  deck  of  a  torpedo 
boat,  in  Fig.  307. 

The  explosive  charge,  carried  in  the  head  of  the  torpedo,  is  fired 
by  percussion  when  the  torpedo  strikes. 

SUBMERSION  MECHANISM. — In  a  chamber  in  rear  of  the  air  tank 
is  the  mechanism  for  regulating  the  r^tl*  ui  Tne  torpedo.  The 
head  of  a  piston.  s^tcd.  on  oy  springs,  protrudes  through  a  central 
hcb  In  one  rear  wall  of  the  chamber  into  another  narrow  chamber 
to  which  the  water  has  access  through  the  holes  in  the  walls  of  the 
torpedo.  The  water  pressure  thus  acts  on  one  side  of  the  piston 


FIG.  30:.. 

and  the  springs  on  the  other.  The  springs  may  be  regulated  to 
exert  a  pressure  on  the  piston  equal  to  the  pressure  of  the  water 
at  any  desired  depth.  At  that  depth  the  piston  will  be  stationary, 
while  at  any  other  depth  it  will  be  moved  forward  or  backward. 
The  piston  is  connected  with  horizontal  diving  rudders  at  the  tail 
of  the  torpedo,  one  on  each  side.  Any  movement  of  the  piston 
caused  by  the  departure  of  the  torpedo  from  the  depth  for  which  it 
is  adjusted  is  communicated  to  these  rudders,  which  act  to  return 
the  torpedo  to  the  desired  depth. 

The  piston  ceases  to  act  when  the  torpedo  is  at  the  fixed  depth, 
whatever  may  be  the  position  of  the  longitudinal  axis  of  the  torpedo. 
As  the  axis  will  not  be  horizontal  when  the  depth  is  reached  the 
torpedo,  if  controlled  by  the  piston  alone,  will  overrun  the  depth 
and  then  return  again  to  it,  and  will  continue  in  this  way  rising  and 
descending.  To  prevent  this  action  a  heavy  pendulum,  in  the 
chamber  with  the  piston,  is  also  connected  with  the  diving  rudders. 
The  pendulum  remains  vertical,  and  at  any  departure  of  the  axis 
of  the  torpedo  from  the  horizontal,  the  diving  rudders  are  turned 
to  correct  the  departure.  The  piston  and  pendulum  together  thus 


588  ORDNANCE   AND  GUNNERY. 

serve  to  keep  the  torpedo  on  an  even  keel  at  the  desired  sub- 
mergence. 

THE  MOTIVE  ENGINES. — The  motive  engines  in  the  next  com- 
partment are  supplied  with  compressed  air  through  pipes  that  lead 
from  the  tank  forward.  The  engines  actuate  two  shafts,  one 
within  the  other,  that  carry  the  propellers.  The  propellers  turn 
in  opposite  directions.  This  arrangement  of  the  propellers  serves 
better  than  any  other  arrangement  to  prevent  rolling  of  the 
torpedo. 

DIRECTING  MECHANISM. — The  compartment  in  rear  of  the  en- 
gine contains  the  device  for  correcting  any  deviation  of  the  torpedo 
from  a  straight  course.  A  small  gyroscope,  with  wheel  about  3 
inches  in  diameter,  is  mounted  under  the  propeller  shaft  with  its 
axis  parallel  to  the  axis  of  the  torpedo.  The  gyroscope  is  set  hi 
motion  by  a  spring-actuated  mechanism  at  the  launching  of  the 
torpedo.  The  axis  of  the  gyroscope  tends  always  to  remain 
parallel  to  its  original  direction,  and  at  any  departure  of  the  axis 
of  the  torpedo  from  its  original  direction  the  gyroscope  actuates 
the  valve  of  a  small  air  steering-engine  which  moves  the  vertical 
rudders  of  the  torpedo  in  such  manner  as  to  bring  the  torpedo  back 
to  its  course. 

SINKING  MECHANISM. — In  order  to  sink  the  torpedo  at  the 
end  of  its  course,  if  it  does  not  strike  its  target,  and  thus  to  pre- 
vent its  falling  into  the  hands  of  the  enemy  or  doing  injury  to 
friends,  a  mechanism  is  provided  which  opens  a  sea-valve  into  the 
eomparatively  empty  chamber  that  contains  the  gyroscope.  The 
water  fills  the  chamber  and  sinks  the  torpedo. 

DATA. — The  Whitehead  torpedo  has  a  diameter  of  18  inches, 
and  a  length  of  about  16  feet.  It  has  a  mean  velocity  of  28  knots 
an  hour  over  a  range  of  2200  yards.  The  charge  of  explosive 
weighs  60  pounds. 

The  Schwarzkopf  torpedo  differs  from  the  Whitehead  only  in 
that  the  body  of  the  torpedo  is  made  of  bronze  instead  of  steel. 

334.  The  Bliss-Leavitt  Torpedo. — The  Bliss-Leavitt  torpedo,  a 
recent  American  construction,  and  in  use  in  the  United  States 
Navy,  is  of  the  same  general  construction  as  the  Whitehead  tor- 
pedo. Improvements  in  the  mechanisms  give  to  this  torpedo 
greater  range  and  greater  accuracy. 


SUBMARINE  MINES  AND   TORPEDOES.  589 

The  air  tank  is  charged  to  a  pressure  of  2225  pounds  per  square 
inch.  The  motor  engine  is  of  the  Curtis  turbine  type  and  makes 
10,000  revolutions  a  minute,  operating  the  two  propellers  at  the 
rate  of  900  turns  a  minute.  A  large  gain  in  power  is  obtained  by  a 
superheating  process  applied  to  the  compressed  air.  An  alcohol 
flame,  automatically  ignited  when  the  torpedo  is  launched,  greatly 
increases  the  expansive  power  of  the  compressed  air  as  it  enters 
the  engine.  The  expansion  is  so  great  that  trouble  has  been  en- 
countered from  the  freezing  of  the  mechanism.  Temperatures  of 
40°  below  zero  have  been  registered  in  some  runs. 

The  gyroscope  controlling  the  vertical  rudders  is  also  of  a  tur- 
bine construction,  and  is  rotated  by  compressed  air  at  the  rate  of 
18,000  revolutions  a  minute.  It  is  much  more  effective  in  main- 
taining the  torpedo  in  a  fixed  course  than  the  spring-actuated 
gyroscope  in  the  Whitehead  torpedo.  The  accuracy  of  the  tor- 
pedo is  therefore  greatly  increased. 

The  Bliss-Leavitt  torpedo  is  made  in  two  sizes,  18  and  21 
inches  in  diameter.  The  21-inch  torpedo  is  about  16j  feet  long. 
It  has  an  extreme  range  of  3500  yards  and  a  mean  speed  over  that 
range  of  28  knots  an  hour.  Over  a  range  of  1200  yards  its  mean 
speed  is  36  knots. 

The  explosive  charge  consists  of  132  pounds  of  wet  guncotton 
containing  25  per  cent  of  water. 

The  firing  mechanism  in  the  point  is  the  same  as  in  the  Howell 
torpedo  described  below. 

The  Howell  Torpedo. — The  Howell  torpedo  was  invented  by 
Admiral  John  A.  Howell,  United  States  Navy.  The  motive  power 
of  the  Howell  torpedo  is  a  solid  flywheel,  w  Fig.  308,  which  is 


FIG.  308. 

caused  to  revolve  at  a  rate  of  10,000  revolutions  a  minute,  before 
the  torpedo  is  launched,  by  a  small  turbine  engine  located  hi  the 
launching  tube.  The  rotation  of  the  flywheel  is  communicated  to 
two  propellers,  one  on  each  side,  through  the  bevel  gears  e  and 
shafts  s. 


590  ORDNANCE  AND  GUNNERY. 

A  device  applied  to  the  propellers  increases  the  pitch  of  the 
blades  as  their  velocity  of  rotation  diminishes,  thus  better  main- 
taining the  speed  of  the  torpedo  at  the  latter  end  of  its  course. 

The  gyroscopic  power  of  the  rotating  flywheel  gives  to  the 
torpedo  great  rigidity  of  direction  in  the  horizontal  plane. 

The  submergence  is  regulated  by  a  hydrostatic  piston  and 
pendulum  that  act  on  the  horizontal  rudders  at  the  tail,  the 
mechanism  being  similar  to  that  described  in  the  Whitehead 
torpedo. 

The  small  screw  at  the  nose  of  the  torpedo  locks  the  firing 
mechanism  in  the  safety  position  until  the  torpedo  has  traveled 
30  or  40  yards  through  the  water.  The  rotation  of  the  screw 
during  this  travel  arms  the  firing  mechanism. 

The  Howell  torpedo  carried  a  charge  of  174  pounds  of  gun- 
cotton.  It  was  fired  by  gunpowder  from  the  launching  tube.  Its 
extreme  effective  range,  1000  yards,  was  so  limited  that  the  tor- 
pedo never  came  into  general  use. 

Towing  Torpedoes. — Towing  torpedoes  are  so  arranged  that 
they  may  be  made  to  diverge  to  a  considerable  extent  on  either 
side  of  the  wake  of  the  towing  vessel,  so  that  this  vessel  may  pass 
clear  of  the  ship  attacked  and  yet  cause  the  torpedo  to  strike. 
Towing  torpedoes  were  used  by  the  Russians  in  their  war  with 
Turkey,  1877,  but  in  no  case  with  success. 

335.  Submarine  Torpedo  Boats. — While  submarine  torpedo 
boats  are  now  used  only  by  the  navy,  it  has  been  recommended 
that  they  be  used  by  the  Coast  Artillery  as  adjuncts  to  the  sub- 
marine mine  systems.  They  will  perform  a  twofold  function  in 
the  mine  fields .  first,  hi  the  inspection  and  repair  of  the  mines  and 
cables  and  other  subaqueous  material,  to  which  access  will  be 
gamed  through  a  diving  compartment  or  caisson  provided  in  the 
boat;  and  second,  in  supplementing  the  fixed  mines  by  defending 
with  the  torpedo  those  channels  or  passages  that  by  reason  of  the 
great  depth  or  the  strength  of  the  current  cannot  be  closed  by 
fixed  mines. 

Submarine  boats  are  of  two  general  classes,  the  diving  boat  and 
the  submersible  boat.  The  diving  boat  submerges  by  inclination 
of  its  longitudinal  axis  effected  through  horizontal  rudders.  It 
rises  by  the  same  means.  The  submersible  boat  sinks  and  rises 


W 


SUBMARINE  MINES  AND  TORPEDOES.  591 

bodily  with  even  keel,  the  movements  being  effected  by  the  ver- 
tical component  of  the  water  pressure  against  inclined  hydro- 
planes projecting  from  both  sides  of  the  boat  and  symmetrically 
disposed  with  respect  to  the  center  of  gravity. 

Both  classes  of  boats  are  provided  with  gasoline  engines  for 
propulsion  on  the  surface,  and  with  electric  motors  for  use  when 
submerged.  When  on  the  surface  the  motors  may  be  used  as 
dynamos  to  charge  the  storage  batteries,  the  power  being  supplied 
by  the  gasoline  engines. 

To  adjust  the  buoyancy,  water  is  pumped  into  or  out  of  the 
ballast  tanks  by  pumps  actuated  by  the  engines  or  motors. 

Air  .compressors  and  tanks  are  also  provided.  The  com- 
pressed air  is  used  for  the  discharge  of  the  torpedoes,  and  to  sup- 
plement the  pumps  in  the  discharge  of  water  ballast. 

The  compressed  air  may  also  be  used  to  renew  the  air  supply 
in  the  vessel  when  submerged.  The  renewal  of  the  air  supply  is, 
however,  usually  not  necessary.  Tests  have  shown  that  the  crew 
does  not  suffer  from  bad  air  when  the  boat  is  hermetically  sealed 
for  long  periods.  In  one  test  7  men  remained  under  water  for 
15  hours  without  change  of  air  and  without  discomfort.  In  an- 
other test  the  boat,  fully  manned,  remained  totally  submerged 
for  12  hours  without  change  of  air.  In  a  recent  test  the  boat, 
with  13  men  aboard,  remained  submerged  at  a  depth  of  about  40 
feet  for  a  period  of  24  hours.  During  the  last  hours  air  was 
drawn  from  the  compressed  air  supply.  The  test  showed  that 
the  boat  could  remain  under  water  for  three  days  before  exhaust- 
ing the  supply  of  air. 

The  Holland  Submarine  Boat. — The  Holland  submarine  boat 
is  the  latest  and  most  successful  boat  of  the  diving  type  of  sub- 
marine. 

The  boat,  Fig.  309,  is  spindle-shaped,  circular  in  cross-section, 
with  its  greatest  diameter  about  one  third  of  its  length  from 
the  bow.  The  single  propeller  is  actuated  by  gasoline  engines 
when  the  boat  is  on  the  surface,  and  by  electric  engines  when  the 
boat  is  awash  or  submerged. 

Submergence  is  effected  by  means  of  horizontal  diving  rudders 
at  the  tail,  arranged  similarly  to  the  diving  rudders  of  the  White- 
head  torpedo. 


592 


ORDNANCE  AND  GUNNERY. 


The  internal  arrangements  of  the  craft  do  not  differ  materially 
from  those  of  the  Lake  submarine  boat  illustrated  in  Fig.  311, 
except  that  the  Holland  boat  contains  no  diving  caisson.  The 
conning  tower  projects  very  slightly  above  the  general  outline  of 
the  boat. 

At  a  recent  government  test  of  the  HoLand  boat  Octopus  an 
average  speed  of  11  knots  an  hour  was  maintained  by  the  boat 
in  cruising  condition  on  the  surface,  and  10  knots  an  hour  when 
awash  and  submerged. 

336.  The  Lake  Submarine  Boat. — The  Lake  submarine  boat 
is  of  the  submersible  type.  An  exterior  view  of  the  Protector,  the 
first  torpedo  boat  of  this  type,  is  shown  in  Fig.  310,  and  an  in- 
terior view  of  the  boat  submerged  is  shown  in  Fig.  311. 


Q 


FIG.  310. 

The  hull  is  spindle-shaped,  67£  feet  long  with  14  feet  beam. 
The  draught,  in  cruising  condition  on  the  surface,  is  12  feet.  The 
displacement  is  136  tons  hi  cruising  trim  and  175  tons  when  sub- 
merged. A  superstructure  is  erected  on  the  hull,  the  top  of  the 
superstructure  forming  the  deck  of  the  boat.  The  space  between 
the  superstructure  and  the  hull  is  occupied  by  the  air,  oil,  and 
ballast  tanks,  and  by  the  tanks  for  the  gasoline  used  in  the  en- 
gines. The  storage  of  the  gasoline  outside  the  hull  greatly  dimin- 
ishes the  chances  of  explosion  from  leaking  gasoline,  or  of  the 
asphyxiation  of  the  crew  from  the  same  cause. 

A  conning  tower  rises  from  the  hull.  A  sighting  hood  projects 
above  the  conning  tower,  and  the  omniscope,  through  which 
vision  is  obtained  hi  all  directions,  rises  3  or  4  feet  above  the 
sighting  hood. 


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SUBMARINE  MINES  AND   TORPEDOES.  593 

The  boat  is  built  to  withstand  an  exterior  pressure  of  75  pounds 
to  the  square  inch,  which  corresponds  to  a  depth  of  about  150 
feet. 

The  boat  is  provided  with  twin  screws. 

SUBMERSION. — Submergence  is  effected  on  an  even  keel;  when 
under  way,  by  inclining  the  four  hydroplanes,  s  Fig.  310,  down- 
ward and  forward;  and  when  the  boat  is  stationary  by  dropping 
the  anchors  at  each  end,  reducing  the  buoyancy  to  less  than  the 
combined  weight  of  the  anchors,  and  then  pulling  the  boat  down- 
ward by  the  anchor  chains.  All  these  operations  are  simply 
effected  from  the  conning  tower. 

The  horizontal  rudder,  R  Fig.  311,  is  used  only  to  counteract 
the  pressure  of  the  water  on  the  front  of  the  conning  tower  when 
the  boat  is  running  submerged. 

The  buoyancy  of  the  boat  is  increased  or  diminished  by  pump- 
big  water  out  of  or  into  the  ballast  tanks.  A  reserve  of  about 
300  pounds  of  buoyancy  is  always  maintained  except  when  run- 
ning on  the  bottom,  and  the  boat  is  held  submerged  either  by  the 
anchors  or,  when  moving,  by  the  water  pressure  on  the  hydro- 
planes. It  may  be  kept  at  any  desired  submergence,  whether 
moving  or  at  rest. 

For  running  on  the  bottom,  wheels  are  provided  which  are 
ordinarily  carried  hi  pockets  in  the  keel  and  which  are  brought 
into  position  under  the  keel  by  hydraulic  mechanism.  The 
wheels  are  simple  rollers  and  the  propellers  move  the  boat,  the 
chief  function  of  the  wheels  being  to  protect  the  bottom  of  the 
boat  against  injury  from  obstacles  on  the  bottom. 

When  the  buoyancy  has  been  destroyed  and  when,  through  any 
accident  to  the  pumps,  it  cannot  be  regained  by  discharging 
ballast,  two  sections  of  the  keel,  N  Fig.  311,  weighing  together 
5  tons,  may  be  dropped  from  the  boat  by  the  turn  of  a  wrench. 
Should  this  not  be  sufficient  to  cause  the  boat  to  rise,  the  two 
anchors,  weighing  half  a  ton  each,  may  be  let  go.  As  a  last  re- 
source the  crew  may  escape  through  the  diving  chamber. 

THE  DIVING  CHAMBER. — The  diving  chamber  hi  the  forward 
compartment  is  a  feature  of  this  boat  that  makes  the  boat  espe- 
cially valuable  for  submarine  mine  work.  An  air  lock  affords 
access  to  the  chamber  from  the  ulterior,  and  a  downwardly-open- 


594  ORDNANCE   AND  GUNNERY. 

ing  watertight  door  in  the  hull  affords  egress  to  the  bottom.  The 
diving  chamber  has  telephonic  communication  with  the  conning 
tower. 

ARMAMENT  AND  SPEED. — The  boat  carries  three  torpedoes,  two 
in  the  tubes  in  the  bow  and  one  in  the>stern  tube.  The  torpedoes 
are  discharged  from  the  tubes  by  compressed  air.  Extra  tor- 
pedoes may  be  carried  in  'the  living  room. 

The  first  boat  of  this  type  made,  in  the  official  trials  by  the 
Russian  Government,  a  speed  of  9.3  knots  an  hour  on  the  surface, 
under  engines  and  motors  combined,  and  8.5  knots  under  engines 
alone.  With  conning  tower  awash  and  under  engines  alone  the 
speed  was  7.4  knots;  and  totally  submerged,  under  electric  motors 
alone,  the  speed  was  5.4  knots.  The  cruising  radius  on  the  surface 
at  full  speed  is  about  350  knots.  The  submerged  cruising  radius, 
with  motors,  is  about  20  knots  at  full  speed  and  30  knots  at  eco- 
nomical speed. 

A  Lake  boat,  with  a  displacement  of  235  tons,  is  now  (May, 
1907)  undergoing  test  by  the  United  States  Government,  and 
boats  with  500  tons  displacement  are  projected. 


TABLES. 

TABLE      I.  LOGARITHMS  OF  THE  X  FUNCTIONS. 

TABLE    II.  HEATS  OF  FORMATION  OF  SUBSTANCES. 

TABLE  III.  SPECIFIC  HEATS  OF  SUBSTANCES. 

TABLE  IV.  DENSITIES  AND  MOLECULAR  VOLUMES  OF  SUBSTANCES. 

TABLE     V.  ATOMIC  WEIGHTS. 

TABLE  VI.  CONVERSION;    METRIC  AND  ENGLISH  UNITS,  TEMPERATURES. 

595 


596 


ORDNANCE  AND   GUNNERY. 


TABLE  I. 

LOGARITHMS  OF  THE  X  FUNCTIONS. 

Subtract  10  from  each  characteristic  greater  than  2. 


X 

logX0 

log*, 

log^2 

log  X3 

logX4 

log*6 

0.001 

9.03899 

5.56162 

6.52263 

8.73764 

9.16405 

8.30001 

0.010 

9.53911 

7.05911 

7.52000 

9.23296 

9.66437 

9.30059 

0.05 

9.88671 

8.09440 

8.20769 

9.56059 

0.01322 

9.99778 

0.10 

0.03494 

S.53009 

8.49515 

9.68493 

0.16295 

0.29663 

0.15 

0.12078 

8.77897 

8.65819 

9.74798 

0.25023 

0.47060 

0.20 

0.18111 

8.95170 

8.77059 

9.78653 

0.31194 

0.59347 

0.25 

0.22750 

9.08291 

8.88541 

9.81206 

0.35965 

0.68834 

0.30 

0.26509 

9.18802 

8.92293 

9.82962 

0.39851 

0.76552 

0.35 

0.29661 

9.27522 

8.97861 

9.84191 

0.43127 

0.83052 

0.40 

0.32372 

9.34942 

9.02570 

9.85051 

0.45956 

0.88660 

0.45 

0.34746 

9.41375 

9.06630 

9.85640 

0.48444 

0.93587 

0.50 

0.36855 

9.47036 

9.10181 

9.86028 

0.50663 

0.97980 

0.55 

0.38750 

9.52077 

9.13327 

9.86260 

0.52665 

1.01937 

0.60 

0.40469 

9.56610 

9.16141 

9.86371 

0.54488 

1.05539 

0.65 

0.42041 

9.60719 

9.18678 

9.86386 

0.56161 

1.08840 

0.70 

0.43489 

9.64471 

9.20982 

9.86325 

0.57705 

1.11887 

0.75 

0.44829 

9.67918 

9.23089 

9.86201 

0.59140 

1.14715 

0.80 

0.46075 

9.71100 

9.25025 

9.86027 

0.60479 

1.17352 

0.85 

0.47241 

9.74052 

9.26812 

9.85811 

0.61733 

1.19821 

0.90 

0.48334 

9.76802 

9.28468 

9.85562 

0.62913 

1.22143 

0.95 

0.49363 

9.79373 

9.30010 

9.85284 

0.64027 

1.24332 

1.00 

0.50334 

9.81784 

9.31450 

9.84984 

0.65081 

1.26404 

1.05 

0.51255 

9.84053 

9.32798 

9.84664 

0.66082 

1.28369 

1.10 

0.52128 

9.86193 

934065 

9.84329 

0.67034 

1.30239 

1.15 

0.52960 

9.88217 

9.35258 

9.83981 

0.67942 

1  .32020 

1.20 

0.53752 

9.90136 

9.36384 

9.83623 

0.68809 

1.33721 

1.25 

0.54508 

9.91958 

9.37449 

9.83256 

0.69640 

1.35348 

1.30 

0.55234 

9.93693 

9.38459 

9.82882 

0.70436 

1.36908 

1.35 

0.55929 

9.95346 

9.39417 

9.82503 

0.71201 

1.38406 

1.40 

0.56597 

9.96926 

9.40329 

9.82119 

0.71936 

1.39846 

1.45 

0.57238 

9.98436 

9.41198 

9.81732 

0.72644 

1.41230 

1.50 

0.57856 

9.99884 

9.42028 

9.81343 

0.73328 

1.42569 

1.55 

0.58452 

0.01272 

9.42820 

9.80953 

0.73988 

1.43858 

1.60 

0.59026 

0.02605 

9.43579 

9.80561 

0.74625 

1.45104 

1.65 

0.59582 

0.03887 

9.44305 

9.80169 

0.75242 

1.46310 

1.70 

0.60119 

0.05122 

9.45003 

9.79777 

0.75840 

1.47478 

1.75 

0.60639 

0.06311 

9.45672 

9.79386 

0.76419 

1.48608 

1.80 

0.61143 

0.07459 

9.46316 

9.78996 

0.76981 

1.49705 

1.85 

0.61632 

0.08567 

9.46935 

9.78607 

0.77527 

1.50770 

1.90 

0.62106 

0.09638 

9.47532 

9.78219 

0.78057 

1.51803 

1.95 

0.62567 

0.10675 

9.48108 

9.77833 

0.78573 

1.52808 

2.0 

0.63015 

0.11678 

9.48663 

9.77449 

0.79075 

1.53788 

2.1 

0.63875 

0.13591 

9.49717 

9.76687 

0.80040 

1.55668 

2.2 

0.64691 

0.15395 

9.50704 

9.75939 

0.80958 

1.57456 

2.3 

0.65467 

0.17097 

9.51630 

9.75193 

0.81833 

1.59158 

2.4 

0.66207 

0.18708 

9.52,501 

9.74461 

0.82668 

1.60783 

TABLES. 


597 


LOGARITHMS  OF  THE  X  FUNCTIONS— Continued. 

Subtract  10  from  each  characteristic  greater  than  2. 


• 

logAo 

log  Xl 

logX2 

log*3 

log  X4 

log*. 

2.5 

0.66914 

0.20236 

9.53322 

9.73740 

0.83467 

1.62338 

2.6 

0.67589 

0.21687 

9.54098 

9.73031 

0.84232 

1.63824 

2.7 

0.68237 

0.23070 

9.54833 

9.72333 

0.84966 

1.65250 

2.8 

0.68859 

0.24389 

9.55531 

9.71645 

0.85673 

1.66623 

2.9 

0.69457 

0.25650 

9.56194 

9.70969 

0.86353 

1.67945 

3.0 

0.70032 

0.26858 

9.56826 

9.70304 

0.87009 

1.69216 

3.1 

0.70587 

0.28014 

9.57427 

9.69650 

0.87642 

1.70442 

3.2 

0.71122 

0.29124 

9.58001 

9.69007 

0.88252 

1.71627 

3.3 

0.71639 

0.30190 

9.58551 

9.68374 

0.88842 

1.72773 

3.4 

0.72140 

0.31217 

9.59077 

9.67752 

0.89416 

1.73882 

3.5 

0.72624 

0.32205 

9.59582 

9.67140 

0.89970 

1.74956 

3.6 

0.73093 

0.33159 

9.60066 

9.66538 

0.90508 

1.75997 

3.7 

0.73548 

0.34079 

9.60532 

9.65946 

0.91027 

1.77004 

3.8 

0.73990 

0.34969 

9.60979 

9.65363 

0.91537 

1.77989 

3.9 

0.74419 

0.35829 

9.61410 

9.64790 

0.92037 

1.78955 

4.0 

0.74836 

0.36662 

9.61825 

9.64225 

0.92510 

-1.79872 

4.2 

0.75637 

0.38250 

9.62613 

9.63122 

0.93432 

1  .81656 

4.4 

0.76398 

0.39745 

9.63348 

9.62053 

0.94308 

1.83349 

4.6 

0.77121 

0.41157 

9.64036 

9.61015 

0.95143 

1.84962 

4.8 

0.77810 

0.42492 

9.64682 

9.60008 

0.95939 

1.86500 

5.0 

0.78469 

0.43759 

9.65290 

9.59029 

0.96700 

1.87971 

5.2 

0.79099 

0.44963 

9.65864 

9.58079 

0.97430 

1.89379 

-  5.4 

0.79703 

0.46110 

9.66407 

9.57153 

0.98130 

1.90730 

5.G 

0.80284 

0.47205 

9.66921 

9.56252 

0.98803 

1.92028 

5.8 

0.80842 

0.48251 

9.67409 

9.55375 

0.99450 

1.93277 

6.0 

0.81379 

0.49253 

9.67874 

9.54521 

1.00074 

1.94479 

6.2 

0.81897 

0.50213 

9.68316 

9.53687 

1.00676 

1.95640  ' 

6.4 

0.82397 

0.51136 

9.68738 

9.52874 

1.01257 

1.96760 

6.6 

0.82881 

0.52022 

9.69142 

9.52081 

1.01819 

1.97844 

6.8 

0.83349 

0.52875 

9.69528 

9.51306 

1.02363 

1.98891 

7.0 

0.83S01 

0.53698 

9.69897 

9.50549 

1  .02890 

1.99905 

7.2 

0.84241 

0.54492 

9.70252 

9.49809 

1.03402 

2.00892 

7.4 

0.84667 

0.55259 

9.70592 

9.49085 

1.03898 

2.01847 

7.6 

0.85081 

0.56000 

9.70919 

9.48377 

1.04379 

2.02776 

7.8 

0.85483 

0.56717 

9.71234 

9.47683 

1.04848 

2.03677 

8.0 

0.85873 

0.57411 

9.71538 

9.47004 

1.05304 

2.04552 

8.2 

0.86254 

0.58084 

9.71830 

9.46341 

1.05748 

2.05408 

8.4 

0.86625 

0.58737 

9.72112 

9.45689 

1.06180 

2.06240 

8.6 

0.86986 

0.59371 

9.72385 

9.45050 

1.06601 

2.07050 

8.8 

0.87338 

0.59986 

9.72648 

9.44424 

1.07012 

2.07841 

9.0 

0.87682 

0.60585 

9.72903 

9.43809 

1.07413 

2.08612 

9.2 

0.88017 

0.61167 

9.73150 

9.43206 

1.07804 

2.09345 

9.4 

0.88345 

0.61734 

9.73390 

9.42614 

1.08187 

2.10100 

9.6 

0.88665 

0.62286 

9.73621 

9.42033 

1.08560 

2.10819 

9.8 

0.88978 

0.62824 

9.73846 

9.41462 

1.08926 

2.11502 

10.0 

0.89284 

0.63349 

9.74065 

9.40901 

1.09283 

2.12209 

10.2 

0.89584 

0.63860 

9.74276 

9.40349 

1.09633 

2.12882 

10.4 

0.89877 

0.64360 

9.74482 

9.39807 

1.09976 

2.13540 

10.6 

0.90165 

0.64848 

9.74683 

9.39274 

1.10312 

2.14186 

10.8 

0.90447 

0.65324 

9.74°77 

9.38749 

1.10640 

2.14818 

598 


ORDNANCE  AND  GUNNERY. 


LOGARITHMS  OF  THE  X  FUNCTIONS— Continued. 

Subtract  10  from  each  characteristic  greater  than  2. 


X 

log  Xo 

log  Zi 

log  A"., 

log-Xa 

log  X, 

log  X6 

11.0 

0.90723 

0.65790 

9.75067 

9.38233 

1.10963 

2.15437 

11.2 

0.90993 

0.66245 

9.75252 

9.37725 

1.11279 

2.16045 

11.4 

0.91259 

0.66691 

9.75432 

9.37225 

1.11589 

2.16642 

11.6 

0.91520 

0.67127 

9.75607 

9.36732 

1.11893 

2.17227 

11.8 

0.91776 

0.67554 

9.75778 

9.36247 

1.12192 

2.17801 

12.0 

0.92027 

0.67972 

9.75945 

9.35770 

1.12485 

2.18364 

12.2 

0.92274 

0.68381 

9.76108 

9.35301 

1.12772 

2.18916 

12.4 

0.92516 

0.68783 

9.76267 

9.34836 

1.13057 

2.19462 

12.6 

0.92754 

0.69176 

9.76422 

9.34379 

1.13335 

2.19996 

12.8 

0.92989 

0.69562 

9.76574 

9.33928 

1.13609 

2.20522 

13.0 

0.93219 

0.69941 

9.76722 

9.33484 

1.13877 

2.21039 

13.2 

0.93446 

0.70313 

9.76867 

933045 

1.14142 

2.21547 

13.4 

0.93669 

0.70678 

9.77009 

9.32613 

1.14402 

2.22047 

13.6 

0.93888 

0.71036 

9.77148 

9.32186 

1.14659 

2.22539 

13.8 

0.94104 

0.71388 

9.77284 

9.31766 

1.14911 

2.23023 

14.0 

0.94317 

0.71734 

9.77417 

9.31350 

1.15159 

2.23400 

14.2 

0.94527 

0.72074 

9.77547 

9.30940 

1.15403 

2.23970 

14.4 

0.94733 

0.72408 

9.77675 

9.30535 

1.15644 

2.24433 

14.6 

0.94936 

0.72736 

9.77800 

9.30136 

1.15882 

2.24888 

14.8 

0.95137 

0.73059 

9.77922 

9.29741 

1.16115 

2.25337 

15.0 

0.95334 

0.73377 

9.78043 

9.29351 

1.16346 

2.25780 

15.2 

0.95529 

0.73689 

9.78160 

9.28966 

1.16573 

2.26216 

15.4 

0.95721 

0.73997 

9.78276 

9.28585 

1.16797 

2.26647 

15.6 

0.95910 

0.74301 

9.78391 

9.28208 

1.17018 

2.27073 

15.8 

0.96097 

0.74599 

9.78501 

9.27837 

1.17236 

2.27495 

16.0 

0.96282 

0.74892 

9.78610 

9.27470 

1.17450 

2.27912 

16.2 

0.96463 

0.75181 

9.78718 

9.27107 

1.17663 

2.28309 

16.4 

0.96643 

0.75466 

9.78823 

9.26748 

1.17872 

2.28711 

16.6 

0.96820 

0.75747 

9.78927 

9.26393 

1.18078 

2.29108 

16.8 

0.96995 

0.76024 

9.79029 

9.26042 

1.18282 

2.29500 

17.0 

0.97168 

0.76297 

9.79129 

9.25695 

1.18483 

2.29886 

17.2 

0.97338 

0.76566 

9.79227 

9.25352 

1.18682 

2.30268 

17.4 

0.97507 

0.76831 

9.79324 

9.25012 

1.18879 

2.30645 

17.6 

0.97673 

0.77093 

9.79419 

9.24676 

1.19072 

2.31017 

17.8 

0.97838 

0.77351 

9.79513 

9.24344 

1.19264 

2.31385 

18.0 

0.98001 

0.77606 

9.79605 

9.24016 

1.19454 

2.317.50 

18.2 

0.98161 

0.77856 

9.79696 

9.23689 

1.19640 

2.32108 

18.4 

0.98320 

0.78104 

9.79785 

9.23367 

1.19825 

2.32463 

18.6 

0.98477 

0.78349 

9.79872 

9.23048 

1.20008 

2.32814 

18.8 

0.98632 

0.78591 

9.79959 

9.22732 

1.20188 

2.33161 

19.0 

0.98785 

0.78829 

9.80044 

9.22419 

1.20367 

2.33.504 

19.2 

0.98937 

0.79065 

9.80128 

9.22109 

1  .20543 

2.33843 

19.4 

0.99086 

0.79296 

9.80210 

9.21803 

1.20717 

2.34177 

19.6 

0.99235 

0.79527 

9.80292 

9.21499 

1  .20891 

2.34510 

19.8 

0.99382 

0.79754 

9.80372 

9.21198 

1.21062 

2.34838 

20.0 

0.99527 

0.79978 

9.80451 

9.20900 

1.21230 

2.35162 

TABLES. 

TABLE  II. 


599 


HEATS   OF   FORMATION,   AT   15°  C.   AND   NORMAL    ATMOSPHERIC 
PRESSURE   (760  MM).     LARGE  CALORIES. 


Name. 

Formula. 

Molec- 
ular 

Weight. 

Heat  given  off,  the  product  being 

Gaseous 

Liquid. 

Solid. 

Dis- 
solved. 

Hydrochloric  acid  .... 
Hydrobromic  acid  
Water  

HCL 
HBr 
H2O 
H,S 
HNO3 
H,S2O3 

so, 

SO3 
H^O, 

CLO 
HC1O4 
CO2 
CO 
N2O 
NO 
N203 
N02 

NA 

K20 
Na2O 
Sb2O3 
Sb205 
KCI 
NaCl 
NH4C1 
CaCl2 
KJ3 
Na.jS 
SbjSs 
(NH4)£ 
KNO3 
NaNo3 
NH4NO3 
K,S04 
Na,,SO4 
Iv-COs 
NaJDQt 
C10H7N02 
C10H8(N02)2 
CIOH.(NOa), 
KC1O3 
NH3 
NS 
CN 
HCN 
KCN 
C2H, 

36.5 
81. 
18. 
34. 
63. 
114. 
64. 
SO. 
98. 

86. 
100.5 
44. 
28. 
44. 
30. 
76. 
46. 
108. 
94. 
62. 
287.2 
329.2 
74.6 
58.5 
53.5 
110. 
110.2 
78. 
335.2 
68. 
101.1 
85. 
80. 
174. 
142. 
138. 
103. 
173. 
218. 
263. 
122.f, 
17. 
46. 
26. 
27. 
65. 
26. 

22. 
9.5 
58.2 
4.8 
34.4 

69.2 
91.8 

-15.2 

94.3 

25.8 
-20.6 
-21.6 
-22.2 
-2.6 
-1.2 

12.2 
-19. 
-37.3 
-29. 

-61.4 

69. 
41.6 

124. 
-30.8 
-16.2 

1.8 
3.6 

-25.4 
-23.8 

70.4 
42.2 

103.6 
124.8 

11.8 
97.2 
100.2 
167.4 
228.8 
105. 
97.3 
76.7 
170. 
102.2 
88.4 
34. 

118.7 
110.6 
87.9 
342.2 
326.4 
278.8 
274.8 
-14.7 
-5.7 
3.3 
94.6 

-31.9 
30.3 

39.3 
29.5 

48.8 
67.2 

141. 
-5.8 

28.6 
164.6 
145.2 

100.8 
96.2 
72.7 
187. 
112.4 
103.2 

56.8 

-33.9 
23.4 

27.4 

Hydrogen  sulphide.  .  .  . 
Nitric  acid       

Hyposulphurous  acid.  . 
Sulphur  dioxide    

Sulphur  trioxide  
Sulphuric  acid  

Hypochlorous  acid  an- 
hydride   

Perchloric  acid    

Carbon  dioxide  

Carbon  monoxide  

Nitrogen  dioxide  

Nitrous  anhydride  

Nitrogen  peroxide  
Nitric  anhydride  

Potassium  oxide  
Sodium  oxide      

Antimonous  oxide  .... 
Antimonic  oxide     .... 

Potassium  chloride.  .  .  . 
Sodium  chloride  

Ammonium  chloride  .  . 
Calcium  chloride  

Potassium  sulphide.  .  . 
Sodium  sulphide  

Antimony  sulphide.  .  . 
Ammonium  sulphide  .  . 
Potassium  nitrate  
Sodium  nitrate   

Ammonium  nitrate.  .  . 
Potassium  sulphate  .  .  . 
Sodium  sulphate.  .  .  . 

Potassium  carbonate  .  . 
Sodium  carbonate  .... 
Nitronaphthalene  
Binitronaphthalene.  .  . 
Trinitronaphthalene  .  . 
Potassium  chlorate  .  .  . 
Ammonia     

Nitrogen  sulphide  
Cyanogen            

Hydrocyanic  acid  
Potassium  cyanide.  .  .  . 
Acetylene            

600 


ORDNANCE  AND  GUNNERY. 
HEATS  OF  FORMATION— Continued. 


Name. 

Formula. 

Molec- 
ular 
Weight. 

Heat  given  off,  the  product  being 

Gaseous 

-15.4 
18.5 
-10.2 
8.6 

53.6 
60.7 

50.5 

65.3 

82.3 

7. 

Liquid. 

Solid. 

Dis- 
solved. 

Ethvlene  

C2H4 
CH4 
C6H6 
C10H16 

^10H8 

Ci4H,0 
CH3OH 

CsH.oH 

C3H7OH 
C8H5OH 
C3H6(OH)3 
C,HM0. 
C8H  08 
n(C8H1208) 
C«H1005 
C2H4O 
C2H5N03 

C,H,(NOs)/>» 

C8H8(N03)6 
C2N202Hg 

c^HpN.^ 

C8H5N02 
C6H4(N02)2 
C8H2(N02)3OH 
C8H2(NO,)3OK 
C8H2(N02)3ONH4 
C8H2(NO2)3ONa 
CeHNsOa 
(C2H<)20 
CHsNO, 
C2H4N208 
C3H02 

C-jOLO, 

C6HnOH 
C5HnNO, 
C6H802 
(CCXNa). 

28. 
16. 
78. 
136. 
128. 
178. 
32. 
46. 
60. 
94. 
92. 
172. 
180. 
n(180.) 
162. 
44. 
91. 
227. 
452. 
284. 
1143. 
123. 
168. 
229. 
267. 
246. 
251. 
167. 
74. 
77. 
152. 
76. 
1008. 
88. 
133. 
62. 
134. 

-3.2 
-17. 

62. 
70.5 
67. 
34.5 
165.5 

56.5 
49.3 
98. 

4.2 

72. 
39.9 
66.9 
127. 

93. 

71. 

-0.9 

-23.7 
-42.4 

36.8 
169.4 
320. 
306. 
n(269.) 
227. 

149. 
-62.9 
624. 
6.9 
12.7 
49.1 
117.5 
80.1 
105.3 
-47.4 

706. 

111.7 
313.8 

64. 
73. 
70. 
32. 
164. 
315. 
303. 

60.1 
50.3 

41. 
107.5 
71.4 
98.9 

78. 

95.8 
113.4 

Methane  

Benzene  

Terebenthene     .... 

Naphthalene  

Anthracene  

Methyl  alcohol   

Ethyl  alcohol  

Propyl  alcohol  

Phenol     

Glycerine     

Mennite  dulcite  

Glucoses  and  isomers  .  . 
Saccharose  and  isomers 
Cellulose  (cotton)  .... 

Aldehyde         

Ethyl  nitrate  

Nitroglycerine  

Nitromannite  

Mercury  fulminate  .... 
Nitrocellulose  (Nn)... 
Nitrobenzene  

Dinitrobenzene       .... 

Picric  acid       

Potassium  picrate  
Ammonium  picrate  .  .  . 
Sodium  picrate  

Diazonitrobenzol  

Ether  

Methyl  nitrate  

Dinitroglycol  

Propyl  glycol  

Nitrocellulose  (N8).... 
Amyl  alcohol  

Amyl  nitrate  

Giycol  

Sodium  oxalate  

TABLES. 

TABLE  III. 

SPECIFIC   HEATS. 


601 


Name. 

Formula. 

Molecular 
Weight. 

Specific  heats  referred  to 

One  Gram. 

Molecular 
Weight. 

As2 
Sb, 
C2 
Hg 
Pb2 
Ag2 
MgO 
Cr2O3 
A12O3 
NH4C1 
KCI 
NaCl 
BaCl, 
CaCL 
AgCl 

FeS 
K4Fe(CN)6 
KNO3 
NaNOa 
Ba(NO3)2 
Sr(N03)2 
Pb(N03)2 
AgNOa 
NH4NO3 

Na.SO, 
CaSO4 
SrS04 
CuSO4 
K2Cr207 
K2C03 
Na2C03 
CaCO3 
BaCO3 
PbCOa 
KClOa 
KC1O4 
H20 
HNOa 
H2SO4 

CTT 
8*16 

C2H5OH 

sb.d 

Si02 

64. 
124. 
150. 
244. 
24. 
200. 
414. 
216. 
40. 
152.8 
103. 
53. 
74.6 
58.5 
207. 
111. 
143. 
110. 
78. 
88. 
430. 
101.1 
85. 
261. 
211. 
330. 
170. 
80. 
174. 
142. 
136. 
183.5 
159.5 
294. 
138. 
106. 
100. 
197. 
26C. 
122.5 
138.5 
18. 
63. 
98. 
78. 
46. 
92. 
287.2 
60.3 

0.203 
0.190 
0.081 
0  .  051 
0.202 
0.033 
0.031 
0.057 
0.244 
0.190 
0.217 
0.373 
0.173 
0.214 
0.090 
0.104 
0.091 
0.091 
0.091 
0.136 
0.280 
0.239 
0.278 
0.150 
0.180 
0.110 
0.143 
0.455 
0.190 
0.229 
0.180 
0.140 
0.134 
0.187 
0.210 
0.270 
0.200 
0.110 
0.141 
0.210 
0.190 
1.000 
0.445 
0.340 
0.440 
0  .  595 
0.591 
0.090 
0.195 

12.8 
11.8 
12.1 
12.4 
4.8 
32.56 
13.2 
12.4 
9.76 
29.00 
22.40 
20.00 
12.89 
12.5 
18.6 
18.4 
13.1 
19.00 
19.00 
11.94 
118.00 
24.20 
23.70 
38.00 
38.00 
36.4 
24.4 
36.4 
33.2 
32.4 
25.4 
24.8 
21.4 
36.4 
30.0 
29.0 
21.0 
21.4 
39.4 
25.7 
26.3 
18.0 
28.0 
33.4 
34.0 
27.3 
54.4 
25.85 
11.76 

Phosphorus      

Lead  

Magnesia  

Chromic  oxide    

Aluminum  oxide    

Ammonium  chloride  

Potassium  chloride  

Sodium  chloride  

Silver  chloride    

Potassium  sulphide  

Sodium  sulphide  

Iron  sulphide        

Potissium  ferro  cyanide  

Potassium  nitrate  

Sodium  nitrate   

Barium  nitrate  

Strontium  nitrate  

Lead  nitrate  

Silver  nitrate        

Potassium  sulphate  

Sodium  sulphate     

Calcium  sulphate     

Strontium  sulphate  

Potassium  bichromate      

Potassium  carbonate       

Sodium  carbonate          

Calcium  carbonate         

Barium  carbonate    

Lead  carbonate  

Potassium  chlorate      

Potassium  perchlorate  

Nitric  acid      

Sulphuric  acid     

Alcohol  

Glycerine          

Antimony  oxide   

Silica    .  .               

602 


ORDNANCE  AND  GUNNERY. 


TABLE  IV. 

DENSITIES  AND  MOLECULAR  VOLUMES. 


Name. 

Formula. 

Molecular 
\\eidit8, 
Jf 

Density. 
D 

Molecular 
Volume 
M 
m  c.c.-p 

Sulphur      

s. 

64. 

2.04 

31.36 

Carbon  

c* 

24. 

(2.  50  diamond 
2  .  27  graphite 

6.85 
10.66 

Potassium  chloride  .  . 

KC1 

74.6 

1.67amorph. 
1.94 

15.28 
38.70 

Sodium  chloride  

NaCl 

58.5 

2.10 

27  20 

Barium  chloride  

BaCL 

207. 

3.70 

56.0 

Strontium  chloride  

SrCL 

158.5 

2.80 

59  0 

Ammonium  chloride  

NH4C1 

53. 

1.53 

35.0 

Potassium  nitrate  

KNO3 

101. 

2.06 

49.0 

Sodium  nitrate  

NaNO3 

85. 

2.24 

39  0 

Barium  nitrate   

Ba(NO3)2 

261. 

3.25 

82  0 

Lead  nitrate  

Pb(NO3)2 

330. 

4.40 

76.0 

Silver  nit  rate  

AgNO3 

170. 

4.35 

39  0 

Ammonium  nitrate  

NH4NO3 

80. 

1.71 

41.0 

Strontium  nitrate  

Sr(NO3), 

211. 

2.93 

71.30 

Potassium  carbonate  
Sodium  carbonate      

K2CO3 
Na2CO3 

138. 
107. 

2.26 
2.47 

62.0 
43  0 

Barium  carbonate..  

Ba,CO3 

197. 

4.30 

46.0 

Strontium  carbonate  

SrCOs 

147.5 

3.62 

40  0 

Calcium  carbonate  

CaCO3 

100. 

2.71 

36  0 

Potassium  sulphate  

KjSO, 

174. 

2.66 

66.0 

Sodium  sulphate    

Na,SO4 

142. 

2.63 

54  0 

Barium  sulphate    

BaSO4 

233. 

2.45 

52  0 

Strontium  sulphate  

SrSO4 

183.5 

3.59 

52.0 

Calcium  sulphate        

CaSO4 

136. 

2.93 

46  0 

Potassium  chlorate  

KC1O3 

122.5 

2.33 

52.6 

Potassium  bichromate  
Antimony  oxide  

K2Cr207 
Sb,O3 

294. 
292. 

2.69 
5.53 

110.0 
53  0 

Antimony  sulphide     

Sb,S3 

334. 

4.42 

75.0 

Calcium  oxide         

CaO 

56. 

3.15 

18.0 

Ammonium  sulphate  
Copper  nitrate  .  

(NH4)J30 

Cu(NO3), 

132. 
192. 

1.76 
2.03 

75.0 
94.5 

Mercuric  oxide     

HgO 

216. 

11.14 

19.38 

Potassium  sulphide  

KJs 

110. 

2.97 

37.0 

Sodium  sulphide  

NaaS 

78. 

2.17 

36.0 

Silica  

S<O2 

60. 

2.65 

23.0 

Potassium  cyanide      

KCN 

65.0 

1.52 

43.0 

TABLES. 


603 


TABLE  V. 
ATOMIC  WEIGHTS. 

The  atomic  weights  in  this  table  are  the  International  Atomic  Weights  (1906) 
modified  to  make  the  atomic  weight  of  hydrogen  unity. 


Element. 

Symbol 

Atomic 
Weight. 

Element. 

Symbol 

Atomic 
Weight. 

Aluminum  

Al 

26.9 

Neon  

Ne 

ion 

Antimony  

Sb 

119.3 

Nickel  

Ni 

KQ     q 

Argon       

A 

39.6 

Niobium  

Nb 

Qq     q 

Arsenic  

As 

74.4 

Nitrogen 

N 

1  q     Q 

Barium  

Ba 

136.4 

Osmium             .  .  . 

Os 

i  on  a 

Beryllium         

Be 

9 

Oxygen 

o 

ICQ 

Bismuth    

Bi 

206  9 

Palladium          .... 

Pd 

•me   7 

Boron      

B 

10  9 

Phosphorus  

p 

qO,    P. 

Bromine        

Br 

79  4 

Platinum 

Pt 

1  qq   q 

Cd 

111  6 

Potassium  

K 

qG     Q 

Caesium          

Cs 

132 

Praseodymium  .  . 

Pr 

1  QQ    4 

Calcium  

Ca 

39  8 

Radium     

Ra 

O9Q   q 

Carbon             

c 

11  9 

Rhodium      .  . 

Ro 

102   9 

Cerium               

Ce 

139 

Rubidium 

Rb 

Q.A  e 

Chlorine      

Cl 

35  2 

Ruthenium  

Ru 

100  9 

Chromium    

Cr 

51   7 

Samarium      

Sm 

148  9 

Cobalt         

Co 

58  5 

Scandium  

Sc 

43  g 

Copper       

Cu 

63  1 

Selenium          .  .  . 

Se 

78  6 

Erbium    

E 

164  8 

Silicon    

Si 

28  2 

Fluorine       

F 

18  9 

Silver  

Ae 

107  1 

Gadolinium 

Gd 

155 

Sodium      .  . 

Na 

22  9 

Gallium      

Ga 

69  5 

Strontium  

Sr 

87 

Germanium  

Ge 

71  9 

Sulphur     

s 

31  8 

Gold       

Au 

195  7 

Tantalum  

Ta 

181  6 

Helium  

He 

4 

Tellurium  

Te 

126  6 

Hydrogen  

H 

1 

Terbium  

Tb 

158  8 

Indium  

In 

113  1 

Thallium    

Tl 

202  6 

Iodine    

I 

125  9 

Thorium    

Th 

230  8 

Indium       

Ir 

191  5 

Thulium    

Tm 

169  7 

Iron            

Fe 

55  5 

Tin     

Sn 

118  1 

Krypton    

Kr 

81  2 

Titanium       

Ti 

47  7 

Lanthanum  

La 

137  9 

Tungsten       

W 

182  6 

Lead         

Pb 

205  4 

Uranium      ,  . 

u 

236  7 

Lithium     

L 

7 

Vanadium           . 

v 

50  g 

Magnesium  

Mg 

24  2 

Xenon          

Xe 

127 

Manganese      

Mn 

54  6 

Ytterbium 

Yb 

171  7 

Mercury          

Hg 

198  5 

Yttrium 

Y 

88  3 

Molybdenum     

Mo 

95  3 

Zinc        

Zn 

64  9 

Neodymium  

Nd 

142.5 

Zirconium  

Zr 

89  9 

604 


ORDNANCE  AND  GUNNERY. 


TABLE  VI. 

CONVERSION:    METRIC    AND     ENGLISH    UNITS,   TEMPERATURES. 


ENGLISH  TO  METRIC. 

METRIC  TO  ENGLISH. 

To  Convert 

Multiply  by 

To  Convert 

Multiply  by 

Inches  to  centimeters  .... 
Inches  to  meters         

2.539978 
0.02539978 
0.3047973 
0.9143918 
1.609329 

6.451484 
0.09290138 
0.8361126 

16.38663 
0.02831609 

0.7645345 
0.9463279 
0.3785311 

0.08479887 
28.34951 
0.4535922 

0.1382537 
0.0703082 
7  .  03082 

Centimeters  to  inches  .... 
Meters  to  inches   

0.39370428 
39  .  370428 
3.280869 
1.093623 
0.6213769 

0.155003 
10.76410 
1.196011 

0.06102537 
35.31561 

1.307985 
1.056716 
2  641791 

15.43236376 
0  .  03527398 
2  .  20462339 

7.233080 
14.22309 

0.1422309 

Feet  to  meters  

Meters  to  feet        

Yards  to  meters  

Meters  to  yards    

Miles  to  kilometers  

Kilometers  to  miles     .... 

Square   inches  to   square 
centimeters  

Square     centimeters     to 
square  inches    

Square  feet  to  square  me- 
ters             

Square  meters  to   square 
feet  

Square  yards  to   square 
meters            

Square  meters  to  square 
yards              

Cubic  inches  to  cubic  cen- 
timeters     

Cubic  centimeters  to  cubic 
inches        

Cubic  feet  to  cubic  meters 
Cubic  yards  to  cubic  me- 
ters              

Cubic  meters  to  cubic  feet. 
Cubic     meters    to    cubic 
yards         

Quarts,  liquid,  to  liters  .... 
Gallons    (231    cu.    in.)   to 
dekaliters    

Liters  to  quarts  (liq.)  

Dekaliters  to  gallons 

Grains  to  grams   

Grams  to  grains  

Ounces  (avoir.)  to  grams.  . 
Pounds  (av.)  to  kilograms. 

Foot-pounds  to  kilogram- 
meters            

Grams  to  ounces  (avoir.).  . 
Kilograms  to  pounds  (av.) 

Kilogrammeters    to    foot- 
pounds   

Pounds  per  sq.  in.  to  kilo- 
grams per  sq  cent  . 

Kilograms  per  sq.  cent,  to 
pound  s  per  sq  in  

Pounds  per  sq.  in.  to  kilo- 
grams per  sq.  decimeter 

Kilograms  per    sq.    deci- 
meter to    pounds   per 
sq    in.                    ... 

TEMPERATURES.— 7>= temperature  Fahrenheit;    Te  =  temperature  centi- 
grade. 

Fahrenheit  to  centigrade,   T0=^  (7/-320). 


Centigrade  to  Fahrenheit,  Tf=-T0  +32°. 


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O'Brine's  Laboratory  Guide  in  Chemical  Analysis 8vo,  2  oo 

O'Driscoll's  Notes  on  the  Treatment  of  Gold  Ores ' 8vo,  2  oo 

Ostwald's  Conversations  on  Chemistry.     Part  One.     (Ramsey.) J2mo,  i  50 

"                  "              "          "            Part  Two.     (TurnbulL) i2mo,  2  oo 

*  Pauli's  Physical  Chemistry  in  the  Service  of  Medicine.     (Fischer.) ....  12010,  i   25 

*  Penfield's  Notes  on  Determinative  Mineralogy  and  Record  of  Mineral  Tests. 

8vo,  paper,  50 

Pictet's  The  Alkaloids  and  their  Chemical  Constitution.     (Biddle.) 8vo,  5  oo 

Pinner's  Introduction  to  Organic  Chemistry.     (Austen.) I2mo.  i  50 

Poole's  Calorific  Power  of  Fuels 8vo,  3  oo 

Prescott  and  Winslow's  Elements  of  Water  Bacteriology,  with  Special  Refer- 
ence to  Sanitary  Water  Analysis I2mo,  i  25 

*  Reisig's  Guide  to  Piece-dyeing 8vo,  25  oo 

Richards  and  Woodman's  Air,  Water,  and  Food  from  a  Sanitary  Standpoint.. 8vo,  2  oo 
Ricketts  and  Russell's  Skeleton  Notes  upon  Inorganic  Chemistry.     (Part  I. 

Non-metallic  Elements.) 8vo,  morocco,  75 

Ricketts  and  Miller's  Notes  on  Assaying 8vo,  3  oo 

Rideal's  Sewage  and  the  Bacterial  Purification  of  Sewage 8vo,  4  oo 

Disinfection  and  the  Preservation  of  Food 8vo,  4  oo 

Riggs's  Elementary  Manual  for  the  Chemical  Laboratory 8vo,  i  25 

Robine  and  Lenglen's  Cyanide  Industry.     (Le  Clerc.) 8vo,  4  oo 

Ruddiman's  Incompatibilities  in  Prescriptions 8vo,  2  oo 

*  Whys  in  Pharmacy I2mo,  i  oo 

Sabin's  Industrial  and  Artistic  Technology  of  Paints  and  Varnish 8vo,  3  oo 

Salkowski's  Physiological  and  Pathological  Chemistry.     (Orndorff.) 8vo,  2  50 

Schimpf's  Text-book  of  Volumetric  Analysis I2mo,  2  50 

Essentials  of  Volumetric  Analysis izmo,  i  25 

*  Qualitative  Chemical  Analysis 8vo,  i  25 

Smith's  Lecture  Notes  on  Chemistry  for  Dental  Students 8vo,  2  50 

Spencer's  Handbook  for  Chemists  of  Beet-sugar  Houses i6mo,  morocco,  3  oo 

Handbook  for  Cane  Sugar  Manufacturers i6mo,  morocco,  3  oo 

Stockbridge's  Rocks  and  Soils 8vo,  2  50 

*  Tillman's  Elementary  Lessons  in  Heat 8vo,  i  so> 

*  Descriptive  General  Chemistry 8vo,  3  oa 

Treadwell's  Qualitative  Analysis.     (Hall.) 8vo,  3  oo 

Quantitative  Analysis.     (Hall.) 8vo,  4  oo 

Turneaure  and  Russell's  Public  Water-supplies 8vo,  5  oo 

5 


Van  Deventer's  Physical  Chemistry  for  Beginners.     (Boltwood.) i2mo,  i  50 

*  Walke's  Lectures  on  Explosives 8vo,  4  oo 

Ware's  Beet-sugar  Manufacture  and  Refining.     Vol.  I Small  8vo,  4  oo 

"               "                                                              Vol.11 SmallSvo,  500 

Washington's  Manual  of  the  Chemical  Analysis  of  Rocks 8vo,  2  oo 

Weaver's  Military  Explosives 8vo,  3  oo 

Wehrenfennig's  Analysis  and  Softening  of  Boiler  Feed-Water 8vo,  4  oo 

Wells's  Laboratory  Guide  in  Qualitative  Chemical  Analysis 8vo,  i  50 

Short  Course  in  Inorganic  Qualitative  Chemical  Analysis  for  Engineering 

Students I2mo,  i  50 

Text-book  of  Chemical  Arithmetic 12010,  i  25 

Whipple's  Microscopy  of  Drinking-water 8vo,  3  50 

Wilson's  Cyanide  Processes 1 2mo,  i  50 

Chlorination  Process I2mo,  I  50 

Winton's  Microscopy  of  Vegetable  Foods 8vo,  7  50 

Wulling's    Elementary    Course    in  Inorganic,  Pharmaceutical,  and  Medical 

Chemistry I2mo,  2  oo 

CIVIL  ENGINEERING. 

BRIDGES   AND    ROOFS.       HYDRAULICS.       MATERIALS   OF    ENGINEERING. 
RAILWAY  ENGINEERING. 

Baker's  Engineers'  Surveying  Instruments. I2mo,  3  oo 

Bixby's  Graphical  Computing  Table Paper  19^X24!  inches.  25 

Breed  and  Hosmer's  Principles  and  Practice  of  Surveying 8vo,  3  oo 

*  Burr's  Ancient  and  Modern  Engineering  and  the  Isthmian  Canal 8vo,  3  50 

Comstock's  Field  Astronomy  for  Engineers 8vo,  2  50 

Crandall's  Text- book  on  Geodesy  and  Least  Squares 8vo,  3  oo 

Davis's  Elevation  and  Stadia  Tables 8vo,  i  oo 

Elliott's  Engineering  for  Land  Drainage I2mo,  i  50 

Practical  Farm  Drainage i2mo,  i  oo 

*Fiebeger's  Treatise  on  Civil  Engineering 8vo,  5  oo 

Flemer's  Phototopographic  Methods  and  Instruments 8vo,  5  oo 

Folwell's  Sewerage.      (Designing  and  Maintenance. ) 8vo,  3  oo 

Freitag's  Architectural  Engineering.     2d  Edition,  Rewritten 8vo,  3  50 

French  and  Ives's  Stereotomy 8vo,  2  50 

Goodhue's  Municipal  Improvements lamo,  i  50 

Gore's  Elements  of  Geodesy 8vo,  2  50 

Hayford's  Text-book  of  Geodetic  Astronomy 8vo,  3  oo 

Bering's  Ready  Reference  Tables  (Conversion  Factors) i6mo,  morocco,  2  50 

Howe's  Retaining  Walls  for  Earth I2mo,  r  25 

*  Ives's  Adjustments  of  the  Engineer's  Transit  and  Level i6mo,  Bds.  25 

Ives  and  Hilts's  Problems  in  Surveying i6mo,  morocco,  i  50 

Johnson's  (J.  B.)  Theory  and  Practice  of  Surveying Small  8vo,  4  oo 

Johnson's  (L.  J.)  Statics  by  Algebraic  and  Graphic  Methods 8vo,  2  oo 

Laplace's  Philosophical  Essay  on  Probabilities.    (Truscott  and  Emory.).  I2mo,  2  oo 

Mahan's  Treatise  on  Civil  Engineering.     (1873.)     (Wood.) 8vo,  5  oo 

*  Descriptive  Geometry 8vo,  i  50 

Merriman's  Elements  of  Precise  Surveying  and  Geodesy 8vo,  2  50 

Merriman  and  Brooks's  Handbook  for  Surveyors i6mo,  morocco,  2  oo 

Nugent's  Plane  Surveying 8vo,  3  50 

Ogden's  Sewer  Design 12010,  2  oo 

Parsons's  Disposal  of  Municipal  Refuse 8vo,  2  oo 

Patton's  Treatise  on  Civil  Engineering 8vo  half  leather,  7  50 

Reed's  Topographical  Drawing  and  Sketching 4to,  5  oo 

Rideal's  Sewage  and  the  Bacterial  Purification  of  Sewage 8vo,  4  oo 

Siebert  and  Biggin's  Modern  Stone-cutting  and  Masonry 8vo,  i  50 


Smith's  Manual  01  Topographical  Drawing.     (McMillan.) 8vo,  2  50 

Sondericker's  Graphic  Statics,  with  Applications  to  Trusses,  Beams,  and  Arches. 

8vo,  2  oo 

Taylor  and  Thompson's  Treatise  on  Concrete,  Plain  and  Reinforced 8vo,  5  oo 

*  Trautwine's  Civil  Engineer's  Pocket-book i6mo,  morocco,  5  oo 

Venable's  Garbage  Crematories  in  America 8vo,  2  oo 

Wait's  Engineering  and  Architectural  Jurisprudence 8vo  6  oo 

Sheep,  6  50 

Law  of  Operations  Preliminary  to  Construction  in  Engineering  and  Archi- 
tecture  8vo,  5  oo 

Sheep,  5  50 

Law  of  Contracts 8vo,  3  oo 

Warren's  Stereotomy — Problems  in  Stone-cutting 8vo,  2  50 

Webb's  Problems  in  the  Use  and  Adjustment  of  Engineering  Instruments. 

i6mo,  morocco,  i  25 

Wilson's  Topographic  Surveying 8vo,  3  50 


BRIDGES  AND  ROOFS. 

Boiler's  Practical  Treatise  on  the  Construction  of  Iron  Highway  Bridges.  .8vo,  2  oo 

*       Thames  River  Bridge 4to,  paper,  5  oo 

Burr's  Course  on  the  Stresses  in  Bridges  and  Roof  Trusses,  Arched  Ribs,  and 

Suspension  Bridges 8vo,  3  50 

Burr  and  Falk's  Influence  Lines  for  Bridge  and  Roof  Computations 8vo,  3  oo 

'  Design  and  Construction  of  Metallic  Bridges 8vo  5  oo 

Du  Bois's  Mechanics  of  Engineering.     Vol.  II Small  4to,  10  oo 

Foster's  Treatise  on  Wooden  Trestle  Bridges 4to,  5  oo 

Fowler's  Ordinary  Foundations 8vo,  3  50 

Greene's  Roof  Trusses 8vo,  i  25 

Bridge  Trusses 8vo,  2  50 

Arches  in  Wood,  Iron,  and  Stone 8vo  2  50 

Howe's  Treatise  on  Arches 8yo,  4  oo 

Design  of  Simple  Roof-trusses  in  Wood  and  Steel , 8vo,  2  oo 

Symmetrical  Masonry  Arches 8vo,  2  50 

Johnson,  Bryan,  and  Turneaure's  Theory  and  Practice  in  the  Designing  of 

Modern  Framed  Structures Small  410,  10  oo 

Merriman  and  Jacoby's  Text-book  on  Roofs  and  Bridges : 

PoTi  I.    Stresses  in  Simple  Trusses 8vo,  2  50 

Pare  IL    Graphic  Statics 8vo,  2  50 

Fart  HI.  Bridge  Design 8vo,  2  50 

Part  IV.   Higher  Structures 8vo,  2  50 

Morison's  Memphis  Bridge 4to,  10  oo 

Waddell's  De  Pontibus,  a  Pocket-book  for  Bridge  Engineers.  .i6mo,  morocco,  2  oo 

*  Specifications  for  Steel  Bridges I2mo,  50 

Wright's  Designing  of  Draw-spans.     Two  parts  in  one  volume 8vo,  3  S<> 

HYDRAULICS. 

Barnes's  Ice  Formation •  •   8vo«  3  oo 

Bazin's  Experiments  upon  the  Contraction  of  the  Liquid  Vein  Issuing  from 

an  Orifice.     (Trautwine.) 8v°.  2  °° 

Bovey's  Treatise  on  Hydraulics 8v°t  5  oo 

Church's  Mechanics  of  Engineering 8vo-  6 

Diagrams  of  Mean  Velocity  of  Water  in  Open  Channels paper,  i  50 


Hydraulic  Motors. 


.8vo,    2  oo 


Coffin's  Graphical  Solution  of  Hydrr.ulic  Problems i6mo,  morocco,    2 

Flather's  Dynamometers,  and  the  Measurement  of  Power izmo,    3  oo 

7 


Folwell's  Water-supply  Engineering 8vo,  4  oo 

FrizelTs  Water-power 8vo,  5  oo 

Fuertes's  Water  and  Public  Health i2mo,  i   50 

Water-filtration  Works i2mo,  2  50 

Ganguillet  and  Kutter's  General  Formula  for  the  Uniform  Flow  of  Water  in 

Rivers  and  Other  Channels.     (Hering  and  Trautwine.; 8vo,  4  oo 

Hazen's  Filtration  of  Public  Water-supply 8vo,  3  oo 

Hazlehurst's  Towers  and  Tanks  for  Water- works 8vo,  2  50 

Herschel's  115  Experiments  on  the  Carrying  Capacity  of  Large,  Riveted,  Metal 

Conduits 8vo,  2  oo 

Mason's  Water-supply.     (Considered  Principally  from  a  Sanitary  Standpoint.) 

8vo,  4  oo 

Merriman's  Treatise  on  Hydraulics 8vo,  5  oo 

*  Michie's  Elements  of  Analytical  Mechanics 8vo,  4  oo 

Schuyler's   Reservoirs   for   Irrigation,   Water-power,   and   Domestic   Water- 
supply Large  8vo,  5  oo 

*  Thomas  and  Watt's  Improvement  of  Rivers 4to,  6  oo 

Turneaure  and  Russell's  Public  Water-supplies 8vo,  5  oo 

Wegmann's  Design  and  Construction  of  Dams 4to,  5  oo 

Water-supply  of  the  City  of  New  York  from  1658  to  1895 4to,  10  oo 

Whipple's  Value  of  Pure  Water Large  12010,  i  oo 

Williams  and  Hazen's  Hydraulic  Tables. 8vo,  i  50 

Wilson's  Irrigation  Engineering Small  8vo,  4  oo 

Wolff's  Windmill  as  a  Prime  Mover 8vo,  3  oo 

Wood's  Turbines 8vo,  2  50 

Elements  of  Analytical  Mechanics 8vo,  3  oo 


MATERIALS  OF  ENGINEERING. 

Baker's  Treatise  on  Masonry  Construction 8vo,  5  oo 

Roads  and  Pavements 8vo,  5  oo 

Black's  United  States  Public  Works Oblong  4to,  5  oo 

*  Bovey's  Strength  of  Materials  and  Theory  of  Structures 8vo,  7  50 

Burr's  Elasticity  and  Resistance  of  the  Materials  of  Engineering 8vo,  7  50 

Byrne's  Highway  Construction 8vo,  5  oo 

Inspection  of  the  Materials  and  Workmanship  Employed  in  Construction. 

i6mo,  3  oo 

Church's  Mechanics  of  Engineering 8vo,  6  oo 

Du  Bois's  Mechanics-of  Engineering.     Vol.  I Small  4to,  7  50 

*Eckel's  Cements,  Limes,  and  Plasters 8vo,  6  oo 

Johnson's  Materials  of  Construction Large  8vo,  6  oo 

Fowler's  Ordinary  Foundations 8vo,  3  50 

Graves's  Forest  Mensuration 8vo,  4  oo 

*  Greene's  Structural  Mechanics 8vo,  2  50 

Keep's  Cast  Iron 8vo,  2  50 

Lanza's  Applied  Mechanics 8vo,  7  So 

Marten's  Handbook  on  Testing  Materials.     (Henning.)     2  vols 8vo,  7  50 

Maurer's  Technical  Mechanics 8vo,  4  oo 

Merrill's  Stones  for  Building  and  Decoration 8vo,  5  oo 

Merriman's  Mechanics  of  Materials 8vo,  5  oo 

*  Strength  of  Materials I2mo,  i  oo 

Metcalf's  Steel.     A  Manual  for  Steel-users I2mo,  2  oo 

Patton's  Practical  Treatise  on  Foundations 8vo,  5  oo 

Richardson's  Modern  Asphalt  Pavements 8vo,  3  oo 

Richey's  Handbook  for  Superintendents  of  Construction i6mo,  mor..  4  oo 

*  Ries's  Clays:  Their  Occurrence,  Properties,  and  Uses 8vo,  5  oo 

Rockwell's  Roads  and  Pavements  in  France I2mo,  i  25 


Sabin's  Industrial  and  Artistic  Technology  of  Paints  acd  Varnish 8vo,  3  oo 

*Schwarz's  Longleaf  Pine  in  Virgin  Forest,.. izmo,  i  25 

Smith's  Materials  of  Machines I2mo,  I  oo 

Snow's  Principal  Species  of  Wood 8vo,  3  50 

Spalding's  Hydraulic  Cement I2mo,  2  oo 

Text-book  on  Roads  and  Pavements I2mo,  2  oo 

Taylor  and  Thompson's  Treatise  on  Concrete,  Plain  and  Reinforced 8vo,  5  oo 

Thurston's  Materials  of  Engineering.     3  Parts 8vo,  8  oo 

Part  I.     Non-«metallic  Materials  of  Engineering  and  Metallurgy 8vo,  2  oo 

Part  II.     Iron  and  Steel 8vo,  3  50 

Part  III.     A  Treatise  on  Brasses,  Bronzes,  and  Other  Alloys  and  their 

Constituents : 8vo,  2  50 

Tillson's  Street  Pavements  and  Paving  Materials 8vo,  4  oo 

Waddell's  De  Pontibus.    (A  Pocket-book  for  Bridge  Engineers.).  .i6mo,  mor.,  2  oo 

*         Specifications  for  Steel  Bridges I2mo,  50 

Wood's  (De  V.)  Treatise  on  the  Resistance  of  Materials,  and  an  Appendix  on 

the  Preservation  of  Timber 8vo,  2  oo 

Wood's  (De  V.)  Elements  of  Analytical  Mechanics 8vo,  3  oo 

Wood's  (M.  P.)  Rustless  Coatings:    Corrosion  and  Electrolysis  of  Iron  and 

SteeL .8vo,  4  oo 


RAILWAY  ENGINEERING. 

Andrew's  Handbook  for  Street  Railway  Engineers 3x5  inches,  morocco,  I  25 

Berg's  Buildings  and  Structures  of  American  Railroads 4to,  5  oo 

Brook's  Handbook  of  Street  Railroad  Location i6mo,  morocco,  I  50 

Butt's  Civil  Engineer's  Field-book i6mo,  morocco,  2  50 

Crandall's  Transition  Curve i6mo,  morocco,  I  50 

Railway  and  Other  Earthwork  Tables 8vo,  I  50 

Dawson's  "Engineering"  and  Electric  Traction  Pocket-book. .  i6mo.  morocco,  5  oo 

Dredge's  History  of  the  Pennsylvania  Railroad:   (1879) Paper,  5  oo 

Fisher's  Table  of  Cubic  Yards Cardboard,  25 

Godwin's  Railroad  Engineers'  Field-book  and  Explorers'  Guide.  .  .  i6mo,  mor.,  2  50 
Hudson's  Tables  for  Calculating  the  Cubic  Contents  of  Excavations  and  Em- 
bankments  ' 8vo,  i  oo 

Molitor  and  Beard's  Manual  for  Resident  Engineers i6mo,  i  oo 

Nagle's  Field  Manual  for  Railroad  Engineers i6mo,  morocco,  3  oo 

Philbrick's  Field  Manual  for  Engineers i6mo,  morocco,  3  oo 

Searles's  Field  Engineering i6mo,  morocco,  3  oo 

Railroad  Spiral i6mo,  morocco,  i  50 

Taylor's  Prismoidal  Formulae  and  Earthwork 8vo,  i  50 

*  Trautwine's  Method  of  Calculating  the  Cube  Contents  of  Excavations  and 

Embankments  by  the  Aid  of  Diagrams 8vo,  2  oo 

The  Field  Practice  of  Laying  Out  Circular  Curves  for  Railroads. 

i2mo,  morocco,  2  50 

Cross-section  Sheet Paper,  25 

Webb's  Railroad  Construction i6mo,  morocco,  5  oo 

Economics  of  Railroad  Construction Large  I2mo,  2  50 

Wellington's  Economic  Theory  of  the  Location  of  Railways Small  8vo,  5  oo 


DRAWING. 

Barr's  Kinematics  of  Machinery 8vo,  2  50 

*  Bartlett's  Mechanical  Drawing 8vo,  3  oo 

*  ««                    "                    "        Abridged  Ed 8vo,  150 

Coolidge's  Manual  of  Drawing 8vo,  paper,  i  oo 

9 


Coolidge  and  Freeman's  Elements  of  General  Drafting  for  Mechanical  Engi- 
neers  Obiong  4to,  2  50 

Durley's  Kinematics  of  Machines 8vo,  4  eo 

Emch's  Introduction  to  Projective  Geometry  and  its  Applications 8vo,  2  50 

Hill's  Text-book  on  Shades  and  Shadows,  and  Perspective STO,  2  oo 

Jamison's  Elements  of  Mechanical  Drawing .' 8vo,  2  50 

Advanced  Mechanical  Drawing 8vo,  2  oo 

Jones's  Machine  Design: 

Part  I.     Kinematics  of  Machinery 8vo,  i  50 

Part  II.     Form,  Strength,  and  Proportions  of  Parts 8vo,  3  oo 

MacCord's  Elements  of  Descriptive  Geometry 8vo,  3  oo 

Kinematics;  or,  Practical  Mechanism 8vo,  5  oo 

Mechanical  Drawing 4to,  4  oo 

Velocity  Diagrams 8vo,  I  50 

MacLeod's  Descriptive  Geometry Small  8vo,  i  50 

*  Mahan's  Descriptive  Geometry  and  Stone-cutting 8vo,  i  50 

Industrial  Drawing.  (Thompson.) 8vo,  3  50 

Moyer's  Descriptive  Geometry 8vo,  2  oo 

Reed's  Topographical  Drawing  and  Sketching 4to,  5  oo 

Reid's  Course  in  Mechanical  Drawing 8vo,  2  oo 

Text-book  of  Mechanical  Drawing  and  Elementary  Machine  Design. 8vo,  3  oo 

Robinson's  Principles  of  Mechanism 8vo,  3  oo 

Schwamb  and  Merrill's  Elements  of  Mechanism 8vo,  3  oo 

Smith's  (R.  S.)  Manual  of  Topographical  Drawing.  (McMillan.) 8vo,  2  50 

Smith  (A.  W.)  and  Marx's  Machine  Design 8vo,  3  oo 

*  Titsworth's  Elements  of  Mechanical  Drawing Oblong  8vo,  i   25 

Warren's  Elements  of  Plane  and  Solid  Free-hand  Geometrical  Drawing.  i2tno,  i  oo 

Drafting  Instruments  and  Operations I2mo,  i  25 

Manual  of  Elementary  Projection  Drawing 1 2mo,  i  50 

Manual  of  Elementary  Problems  in  the  Linear  Perspective  of  Form  and 

Shadow 1 2 mo,  i  oo 

Plane  Problems  in  Elementary  Geometry I2mo,  i   25 

Primary  Geometry. I2mo,  75 

Elements  of  Descriptive  Geometry,  Shadows,  and  Perspective '.8vo,  3  50 

General  Problems  of  Shades  and  Shadows 8vo,  3  oo 

Elements  of  Machine  Construction  and  Drawing 8vo,  7  50 

Problems,  Theorems,  and  Examples  in  Descriptive  Geometry 8vo,  2  50 

Weisbach's    Kinematics    and    Power    of    Transmission.        (Hermann    and 

Klein.) 8vo,  5  oo 

Whelpley's  Practical  Instruction  in  the  Art  of  Letter  Engraving i2mo,  2  oo 

Wilson's  (H.  M.)  Topographic  Surveying 8vo,  3  50 

Wilson's  (V.  T.)  Free-hand  Perspective 8vo.  2  50 

Wilson's  (V.  T.)  Free-hand  Lettering 8vo,  i  oo 

Woolf's  Elementary  Course  in  Descriptive  Geometry Large  8vo,  3  oo 


ELECTRICITY  AND  PHYSICS. 

*  Abegg's  Theory  of  Electrolytic  Dissociation.     (Von  Ende.) I2mo,  i  25 

Anthony  and  Brackett's  Text-book  of  Physics.     (Magie.) Small  8vo  3  oo 

Anthony's  Lecture-notes  on  the  Theory  of  Electrical  Measurements.  . .  .  I2mo,  i  oo 

Benjamin's  History  of  Electricity 8vo,  3  oo 

Voltaic  Cell 8vo,  3  oo 

Classen's  Quantitative  Chemical  Analysis  by  Electrolysis.     (Boltwood.).8vo,  3  oo 

*  Collins's  Manual  of  Wireless  Telegraphy I2mo,  i  50 

Morocco,  2  oo 

Crehore  and  Squier's  Polarizing  Photo-chronograph STO,  3  oo 

*  Danneel's  Electrochemistry.     (Merriam.) I2mo,  i  25 

Dawson's  "Engineering"  and  Electric  Tractioa  Pocket-book.  i6mo,  morocco,  5  <>• 

10 


Dolezalek's    Theory   of    the   Lead   Accumulator    (Storage   Battery).      (Von 

Ende. ) 1 21110,  2  50 

Duhem's  Thermodynamics  and  Chemistry.     (Burgess.) 8vo,  4  oo 

Flather's  Dynamometers,  and  the  Measurement  of  Power lamo,  3  oO 

Gilbert's  De  Magnete.     (Mottelay.) 8vo,  2  50 

Hanchett's  Alternating  Currents  Explained I2mo,  i  oo 

Bering's  Ready  Reference  Tables  (Conversion  Factors) i6mo,  morocco,  2  50 

Holman's  Precision  of  Measurements 8vo,  2  oo 

Telescopic   Mirror-scale  Method,  Adjustments,  and  Tests.  . .  .Large  8vo,  75 

Kinzbrunner's  Testing  of  Continuous-current  Machines 8vo,  2  oo 

Landauer's  Spectrum  Analysis.     (Tingle.) 8vo,  3  oo 

Le  Chatelier's  High-temperature  Measurements.  (Boudouard — Burgess.)  I2mo,  3  oo 

Lob's  Electrochemistry  of  Organic  Compounds.     (Lorenz.) 8vo,  3  oo 

*  Lyons'?  Treatise  on  Electromagnetic  Phenomena.   Vols.  I.  and  II.  8vo,  each,  6  oo 

*  Michie's  Elements  of  Wave  Motion  Relating  to  Sound  and  Light 8vo,  4  oo 

Niaudet's  Elementary  Treatise  on  Electric  Batteries.     (Fishback.) I2mo,  2  50 

*  Parshall  and  Hobart's  Electric  Machine  Design 4to,  half  morocco,  12  50 

Reagan's  Locomotives:    Simple,  Compound,  and  Electric.      New  Edition. 

Large  I2mo,  3  50 

*  Rosenberg's  Electrical  Engineering.     (Haldane  Gee — Kinzbrunner.).  .  .8vo,  2  oo 

Ryan,  Norris,  and  Hoxie's  Electrical  Machinery.     VoL  1 8vo,  2  50 

Thurston's  Stationary  Steam-engines 8vo,  2  50 

*  Tillman's  Elementary  Lessons  in  Heat 8vo,  i  50 

Tory  and  Pitcher's  Manual  of  Laboratory  Physics Small  8vo,  2  oo 

Ulke's  Modern  Electrolytic  Copper  Refining 8vo,  3  oo 


LAW. 

*  Davis's  Elements  of  Law 8vo,  2  50 

*  Treatise  on  the  Military  Law  of  United  States 8vo,  7  oo 

*  Sheep,  7  50 

*  Dudley's  Military  Law  and  the  Procedure  of  Courts-martial  .  .  .  .Large  I2mo,  2  50 

Manual  for  Courts-martial i6mo,  morocco,  i  50 

Wait's  Engineering  and  Architectural  Jurisprudence 8vo,  6  oo 

Sheep,  6  50 

Law  of  Operations  Preliminary  to  Construction  in  Engineering  and  Archi- 
tecture  8vo  5  oo 

Sheep,  5  5<> 

Law  of  Contracts 8vo,  3  oo 

Winthrop's  Abridgment  of  Military  Law I2mo,  2  50 


MANUFACTURES. 

Bernadou's  Smokeless  Powder — Nitro-cellulose  and  Theory  of  the  Cellulose 

Molecule I2mo,  2  50 

Bolland's  Iron  Founder I2mo,  2  50 

The  Iron  Founder,"  Supplement I2mo,  2  50 

Encyclopedia  of  Founding  and  Dictionary  of  Foundry  Terms  Used  in  the 

Practice  of  Moulding i  zmo,  3  oo 

*  Claassen's  Beet-sugar  Manufacture.    (Hall  and  Rolfe.) 8vo,  3  oo 

*  Eckel's  Cements,  Limes,  and  Plasters 8vo,  6  oo 

Eissler's  Modern  High  Explosives 8vo,  4  oo 

Effront's  Enzymes  and  their  Applications.     (Prescott.) 8vo,  3  oo 

Fitzgerald's  Boston  Machinist I2mo,  i  oo 

Ford's  Boiler  Making  for  Boiler  Makers i8mo,  r  oo 

Herrick's  Denatured  or  Industrial  Alcohol 8vo,  40* 

Hopkin's  Oil-chemists'  Handbook 8vo,  3  oe 

Keep's  Cast  Iron 8v»,  2  s» 

11 


Leach's  The  Inspection  and  Analysis  of  Food  with  Special  Reference  to  State 

Control. Large  8vo,  7  50 

*  McKay  and  Larsen's  Principles  and  Practice  of  Butter-making 8vo,  i  50 

Matthews's  The  Textile  Fibres,   ad  Edition,  Rewritten  8vo,  4  oo 

Metcalf's  Steel,     A  Manual  for  Steel-users I2mo,  2  oo 

Metcalfe'f  Cost  of  Manufactures — And  the  Administration  of  Workshops. 8vo,  5  oo 

Meyer's  Modern  Locomotive  Construction 4to,  10  oo 

Morse's  Calculations  used  in  Cane-sugar  Factories i6mo,  morocco,  i  50 

*  Reisig's  Guide  to  Piece-dyeing, 8vo,  25  oo 

Rice's  Concrete-block  Manufacture 8vo,  2  oo 

Sabin's  Industrial  and  Artistic  Technology  of  Paints  and  Varnish 8vo,  3  oo 

Smith's  Press-working  of  Metals 8vo,  3  oo 

Spalding's  Hydraulic  Cement I2mo,  2  oo 

Spencer's  Handbook  for  Chemists  of  Beet-sugar  Houses i6mo  morocco,  3  oo 

Handbook  for  Cane  Sugar  Manufacturers i6mo  morocco,  3  oo 

Taylor  and  Thompson's  Treatise  on  Concrete,  Plain  and  Reinforced 8vo,  5  oo 

Thurston's  Manual  of  Steam-boilers,  their  Designs,  Construction  and  Opera- 
tion  8vo,  5  oo 

*  Walke's  Lectures  on  Explosives 8vo,  4  oo 

Ware's  Beet-sugar  Manufacture  and  Refining.    Vol.1 . .     Small  8vo,  4  oo 

Vol.  II 8vo,  5  oo 

Weaver's  Military  Explosives 8vo,  3  oo 

West's  American  Foundry  Practice I2mo,  2  50 

Moulder's  Text-book I2mo,  2  50 

Wolff's  Windmill  as  a  Prime  Mover 8vo,  3  oo 

Wood's  Rustless  Coatings:   Corrosion  and  Electrolysis  of  Iron  and  Steel.  .8vo,  4  oo 


MATHEMATICS. 

Baker's  Elliptic  Functions. , 8vo,  i  50 

*  Bass's  Elements  of  Differential  Calculus I2mo,  4  oo 

Briggs's  Elements  of  Plane  Analytic  Geometry ismo,  i  oo 

Compton's  Manual  of  Logarithmic  Computations i2mo  r  50 

Davis's  Introduction  to  the  Logic  of  Algebra 8vo,  i  50 

*  Dickson's  College  Algebra Large  i2moi  i  50 

*  Introduction  to  the  Theory  of  Algebraic  Equations Large  I2mo,  i   25 

Emch's  Introduction  to  Projective  Geometry  and  its  Applications 8vo  2  50 

Halsted's  Elements  of  Geometry 8vo,  i  75 

Elementary  Synthetic  Geometry 8vo,  i  50 

*  Rational  Geometry 1 21110.  i   50 

*  Johnson's  (J.  B.)  Three-place  Logarithmic  Tables:  Vest-pocket  size,  pa  per,  15 

100  copies  for  5  oo 

*  Mounted  on  heavy  cardboard,  8X 10  inches,  25 

10  copies  for  2  oo 

Johnson's  (W.  W.)  Elementary  Treatise  on  Differential  Calculus .  . Small  8vo,  3  oo 

Elementary  Treatise  on  the  Integral  Calculus SmalfSvo,  i  50 

Johnson's  (W.  W.)  Curve  Tracing  in  Cartesian  Co-ordinates. lamo,  i  oo 

Johnson's  (W.  W.)  Treatise  on  Ordinary  and  Partiaf  Differential  Equations. 

Small  8vo,  3  50 

Johnson's  (W.  W.)  Theory  of  Errors  and  the  Method  of  Least  Squares.  I2mo,  i  50 

*  Johnson's  (W.  W.)  Theoretical  Mechanics I2mo,  3  oo 

Laplace's  Philosophical  Essay  on  Probabilities.    (Truscott  and  Emory.).  i2mo,  2  oo 

*  Ludlow  and  Bass.     Elements  of  Trigonometry  and  Logarithmic  and  Other 

Tables 8vo,  3  oo 

Trigonometry  and  Tables  published  separately Each,  2  oc 

*  Ludlow's  Logarithmic  and  Trigonometric  Tables 8vo  i  oo 

Manning's  Irrational  Numbers  and  their  Representation  by  Sequences  and  Series 

i2mo,  i  25 

13 


Mathematical  Monographs.     Edited  by  Mansfield  Merriman  and  Robert 

S.  Woodward Octavo,  each     I  oo 

No.  i.  History  of  Modern  Mathematics,  by  David  Eugene  Smith. 
No.  2.  Synthetic  Projective  Geometry,  by  George  Bruce  Halsted. 
No.  3.  Determinants,  by  Laenas  Gifford  Weld.  No.  4.  Hyper- 
bolic Functions,  by  James  McMahon.  No.  5.  Harmonic  Func- 
tions, by  William  E.  Byerly.  No.  6.  Grassmann's  Space  Analysis, 
by  Edward  W.  Hyde.  No.  7.  Probability  and  Theory  of  Errors, 
by  Robert  S.  Woodward.  No.  8.  Vector  Analysis  and  Quaternions, 
by  Alexander  Macfarlane.  No.  9.  Differential  Equations,  by 
William  Woolsey  Johnson.  No.  10.  The  Solution  of  Equations, 
by  Mansfield  Merriman.  No.  u.  Functions  of  a  Complex  Variable, 
by  Thomas  S.  Fiske. 

Maurer's  Technical  Mechanics 8vo,    4  oo 

Merriman's  Method  of  Least  Squares 8vo,    2  oe 

Rice  and  Johnson's  Elementary  Treatise  on  the  Differential  Calculus. .  Sm.  8vo,    3  oo 

Differential  and  Integral  Calculus.     2  vols.  in  one Small  8vo,    2  50 

*  Veblen  and  Lennes's  Introduction  to  the  Real  Infinitesimal  Analysis  of  One 

Variable 8vo,   2  oo 

Wood's  Elements  of  Co-ordinate  Geometry 8vo,    2  oo 

Trigonometry:  Analytical,  Plane,  and  Spherical i2mo,    i  oo 


MECHANICAL  ENGINEERING. 

MATERIALS  OF  ENGINEERING,  STEAM-ENGINES  AND  BOILERS. 

Bacon's  Forge  Practice 12010,  i  50 

Baldwin's  Steam  Heating  for  Buildings I2mo,  2  50 

Barr's  Kinematics  of  Machinery 8vo,  2  50 

*  Bartlett's  Mechanical  Drawing 8vo,  3  oo 

*  "                                     "        Abridged  Ed 8vo,  i  50 

Benjamin's  Wrinkles  and  Recipes I2mo,  2  oo 

Carpenter's  Experimental  Engineering 8vo,  6  oo 

Heating  and  Ventilating  Buildings 8vo,  4  oo 

Clerk's  Gas  and  Oil  Engine Small  8vo,  4  oo 

Coolidge's  Manual  of  Drawing 8vo,  paper,  i  oo 

Coolidge  and  Freeman's  Elements  of  General  Drafting  for  Mechanical  En- 
gineers   Oblong  4to,  2  50 

Cromwell's  Treatise  on  toothed  Gearing I2mo,  i  50 

Treatise  on  Belts  and  Pulleys I2mo,  i  50 

Durley's  kinematics  of  Machines 8vo,  4  oo 

Flather's  Dynamometers  and  the  Measurement  of  Power 12010,  3  oo 

Rope  Driving I2mo,  2  oo 

Gill's  Gas  and  Fuel  Analysis  for  Engineers izmo,  r  25 

Hall's  Car  Lubrication izmo,  i  oo 

Bering's  Ready  Reference  Tables  (Conversion  Factors) i6mo,  morocco,  2  50 

Button's  The  Gas  Engine 8vo,  5  oo 

Jamison's  Mechanical  Drawing 8vo,  2  50 

Jones's  Machine  Design: 

Part  I.     Kinematics  of  Machinery 8vo,  i  50 

Part  n.     Form,  Strength,  and  Proportions  of  Parts 8vo,  3  oo 

Kent's  Mechanical  Engineers'  Pocket-book i6mo,  morocco,  5  oo 

KBIT'S  Power  and  Power  Transmission. 8vo,  2  oo 

Leonard's  Machine  Shop,  Tools,  and  Methods 8vo,  4  oo 

*  Lorenz's  Modern  Refrigerating  Machinery.    (Pope,  Haven,  and  Dean.)  .  .  8vo,  4  oo 
MacCord's  Kinematics ;  cr,  Practical  Mechanism. 8vo,  5  oo 

Mechanical  Drawing 4to,  4  oo 

Velocity  Diagrams 8vo,  i  50 

13 


MacFarland's. Standard  Reduction  Factors  for  Gases 8vo,  i  50 

Mahan's  Industrial  Drawing.  (Thompson. ) 8vo,  3  50 

Poole's  Calorific  Power  of  Fuels ; 8vo,  3  oo 

Reid's  Course  in  Mechanical  Drawing 8vo,  2  oo 

Text-book  of  Mechanical  Drawing  and  Elementary  Machine  Design. 8vo,  3  oo 

Richard's  Compressed  Air i2mo,  i  50 

Robinson's  Principles  of  Mechanism 8vo,  3  oo 

Schwamb  and  Merrill's  Elements  of  Mechanism 8vo,  3  oo 

Smith's  (O.)  Press-working  of  Metals 8vo,  3  oo 

Smith  (A.  W.)  and  Marx's  Machine  Design 8vo,  3  oo 

Thurston's  Treatise  on  Friction  and  Lost  Work  in  Machinery  and  Mill 

Work 8vo,  3  oo 

Animal  as  a  Machine  and  Prime  Motor,  and  the  Laws  of  Energetics .  i2mo,  i  oo 

Tillson's  Complete  Automobile  Instructor i6mo,  i  50 

Morocco,  2  oo 

Warren's  Elements  of  Machine  Construction  and  Drawing 8vo,  7  50 

Weisbach's  Kinematics  and  the  Power  of  Transmission.  (Herrmann — 

Klein.) 8vo,  5  oo 

Machinery  of  Transmission  and  Governors.  (Herrmann — Klein.).  .8vo,  5  oo 

Wolff's  Windmill  as  a  Prime  Mover 8vo,  3  oo 

Wood's  Turbines 8vo,  2  50 


MATERIALS  OF   ENGINEERING. 

*  Bovey's  Strength  of  Materials  and  Theory  of  Structures 8vo,  7  50 

Burr's  Elasticity  and  Resistance  of  the  Materials  of  Engineering.    6th  Edition. 

Reset ; 8vo,  7  50 

Church's  Mechanics  of  Engineering 8vo,  6  oo 

*  Greene's  Structural  Mechanics  . 8vo,  2  50 

Johnson's  Materials  of  Construction 8vo,  6  oo 

Keep's  Cast  Iron 8vo,  2  50 

Lanza's  Applied  Mechanics 8vo,  7  50 

Martens's  Handbook  on  Testing  Materials.     (Henning.) 8vo,  7  50 

Maurer's  Technical  Mechanics 8vo,  4  oo 

Merriman's  Mechanics  of  Materials 8vo,  5  oo 

*  Strength  of  Materials I2mo,  i  oo 

Metcalf's  Steel.     A  Manual  for  Steel-users I2mo,  2  oo 

Sabin's  Industrial  and  Artistic  Technology  of  Paints  and  Varnish 8vo,  3  oo 

Smith's  Materials  of  Machines I2mo,  r  oo 

Thurston's  Materials  of  Engineering 3  vols.,  8vo,  8  oo 

Part  II.     Iron  and  Steel 8vo,  3  50 

Part  III.     A  Treatise  on  Brasses,  Bronzes,  and  Other  Alloys  and  their 

Constituents 8vo,  2  50 

Wood's  (De  V.)  Treajtise  on  the  Resistance  of  Materials  and  an  Appendix  on 

the  Preservation  of  Timber 8vo,  2  oo 

Elements  of  Analytical  Mechanics 8vo,  3  oo 

Wood's  (M.  P.)  Rustless  Coatings:    Corrosion  and  Electrolysis  of  Iron  and 

Steel 8vo,  4  oo 

STEAM-ENGINES  AND  BOILERS. 

Berry's  Temperature-entropy  Diagram I2mo,  i  25 

Carnot's  Reflections  on  the  Motive  Power  of  Heat.     (Thurston.) 121110,  i  50 

Creighton's  Steam-engine  and  other  Heat-motors — 8vo,  500 

Dawson's  "Engineering"  and  Electric  Traction  Pocket-book.  . .  .i6mo,  mor.,  5  oo 

Ford's  Boiler  Making  for  Boiler  Makers i8mo,  i  oo 

Goss's  Locomotive  Sparks 8vo,  2  oo 

Locomotive  Performance 8vo,  5  oo 

Hemenway's  Indicator  Practice  and  Steam-engine  Economy I2mo,  2  oo 

14 


Button's  Mechanical  Engineering  of  Power  Plants 8vo,  5  oo 

Heat  and  Heat-engines 8vo,  5  oo 

Kent's  Steam  boiler  Economy 8vo,  4  oo 

Kneass's  Practice  and  Theory  of  the  Injector 8vo,  i  50 

MacCord's  Slide-valves 8vo,  2  oo 

Meyer's  Modern  Locomotive  Construction 4to,  10  oo 

Peabody's  Manual  of  the  Steam-engine  Indicator I2mo,  x  50 

Tables  of  the  Properties  of  Saturated  Steam  and  Other  Vapors    8vo,  i  oo 

Thermodynamics  of  the  Steam-engine  and  Other  Heat-engines 8vo,  5  oo 

Valve-gears  for  Steam-engines 8vo,  2  50 

Peabody  and  Miller's  Steam-boilers 8vo,  4  oo 

Pray's  Twenty  Years  with  the  Indicator Large  8vo,  2  50 

Pupin's  Thermodynamics  of  Reversible  Cycles  in  Gases  and  Saturated  Vapors. 

(Osterberg.) I2mo,  i  23 

Reagan's  Locomotives:    Simple,  Compound,  and  Electric.     New  Edition. 

Large  12 mo,  3  50 

Rontgen's  Principles  of  Thermodynamics.     (Du  Bois.) 8vo,  5  o« 

Sinclair's  Locomotive  Engine  Running  and  Management I2mo,  2  oo 

Smart's  Handbook  of  Engineering  Laboratory  Practice I2mo,  2  50 

Snow's  Steam-boiler  Practice 8vo,  3  oo 

Spangler's  Valve-gears 8vo,  2  50 

Notes  on  Thermodynamics i2mo,  i  oo 

Spangler,  Greene,  and  Marshall's  Elements  of  Steam-engineering 8vo,  3  oo 

Thomas's  Steam-turbines 8vo,  3  50 

Thurston's  Handy  Tables 8vo,  i  50 

Manual  of  the  Steam-engine 2  vols.,  8vo,  10  oo 

Part  I.     History,  Structure,  and  Theory 8vo,  6  oo 

Part  II.     Design,  Construction,  and  Operation 8vo,  6  oo 

Handbook  of  Engine  and  Boiler  Trials,  and  the  Use  of  the  Indicator  and 

the  Prony  Brake 8vo,  5  oo 

Stationary  Steam-engines 8vo,  2  50 

Steam-boiler  Explosions  in  Theory  and  in  Practice I2mo,  i  50 

Manual  of  Steam-boilers,  their  Designs,  Construction,  and  Operation .  8vo,  5  oo 

Wehrenfenning's  Analysis  and  Softening  of  Boiler  Feed-water  (Patterson)  8vo,  4  oo 

Weisbach's  Heat,  Steam,  and  Steam-engines.     (Du  Bois.) 8vo,  5  oo 

Whitham's  Steam-engine  Design 8vo,  5  oo 

Wood's  Thermodynamics,  Heat  Motors,  and  Refrigerating  Machines.  .  .8vo,  4  oo 


MECHANICS   AND   MACHINERY. 

Barr's  Kinematics  of  Machinery 8vo,  2  50 

*  Bovey's  Strength  of  Materials  and  Theory  of  Structures   8vo,  7  50 

Chase's  The  Art  of  Pattern-making i2mo,  2  50 

Church's  Mechanics  of  Engineering 8vo,  6  oo 

Notes  and  Examples  in  Mechanics 8vo,  2  oo 

Compton's  First  Lessons  in  Metal-working izmo,  i  50 

Compton  and  De  Groodt's  The  Speed  Lathe 12010,  i  50 

Cromwell's  Treatise  on  Toothed  Gearing , i2mo,  i  50 

Treatise  on  Belts  and  Pulleys : I2mo,  i  50 

Dana's  Text-book  of  Elementary  Mechanics  for  Colleges  and  Schools.  .  I2mo,  i  50 

Dingey's  Machinery  Pattern  Making I2mo,  2  oo 

Dredge's  Record  of  the   Transportation  Exhibits  Building  of  the  World's 

Columbian  Exposition  of  1893 4to  half  morocco,  5  oo 

Du  Bois's  Elementary  Principles  of  Mechanics: 

Vol.      I.     Kinematics 8vo,  3  50 

VoL    II.     Statics 8vo.  4  oo 

Mechanics  of  Engineering.     Vol.    I Small  4to,  7  50 

Vol.  II Small  4to,  10  oo 

Durley's  Kinematics  of  Machines 8vo,  4  oo 

15 


Fitzgerald's  Boston  Machinist i6mo,  I  oo 

Flather's  Dynamometers,  and  the  Measurement  of  Power i2mo,  3  oo 

Rope  Driving 12010,  2  oo 

Goss's  Locomotive  Sparks 8vo,  2  oo 

Locomotive  Performance 8vo,  5  oo 

*  Greene's  Structural  Mechanics 8vo,  2  50 

Hall's  Car  Lubrication izrno,  i  oo 

Holly's  Art  of  Saw  Filing i8mo,  75 

James's  Kinematics  of  a  Point  and  the  Rational  Mechanics  of  a  Particle. 

Small  8vo,  2  oo 

*  Johnson's  (W.  W.)  Theoretical  Mechanics izmo,  3  oo 

Johnson's  (L.  J.)  Statics  by  Graphic  and  Algebraic  Methods 8vo,  2  oo 

Jones's  Machine  Design: 

Part    I.     Kinematics  of  Machinery 8vo,  i  50 

Part  II.     Form,  Strength,  and  Proportions  of  Parts 8vo,  3  oo 

Kerr's  Power  and  Power  Transmission 8vo,  2  oo 

Lanza's  Applied  Mechanics 8vo,  7  50 

Leonard's  Machine  Shop,  Tools,  and  Methods ;  .8vo,  4  oo 

*  Lorenz's  Modern  Refrigerating  Machinery.     (Pope,  Haven,  and  Dean.). 8vo,  4  oo 
MacCord's  Kinematics;   or,  Practical  Mechanism 8vo,  5  oo 

Velocity  Diagrams 8vo,  i   50 

*  Martin's  Text  Book  on  Mechanics,  VoL  I,  Statics I2mo,  i   25 

Maurer's  Technical  Mechanics 8vo,  4  oo 

Merriman's  Mechanics  of  Materials 8vo,  5  oo 

*  Elements  of  Mechanics I2mo,  i  oo 

*  Michie's  Elements  of  Analytical  Mechanics 8vo,  4  oo 

*  Parshalland  Hobart's  Electric  Machine  Design 4to,  half  morocco,  12  50 

Reagan's  Locomotives :  Simple,  Compound,  and  Electric.     New  Edition. 

Large  I2mo,  3  oo 

Reid's  Course  in  Mechanical  Drawing 8vo,  2  oo 

Text-book  of  Mechanical  Drawing  and  Elementary  Machine  Design. 8vo,  3  oo 

Richards's  Compressed  Air I2mo,  i   50 

Robinson's  Principles  of  Mechanism 8vo,  3  oo 

Ryan,  Norris,  and  Hoxie's  Electrical  Machinery.     VoL  1 8vo,  2  50 

Sanborn's  Mechanics :  Problems Large  I2mo,  i   50 

Schwamb  and  Merrill's  Elements  of  Mechanism 8vo,  3  oo 

Sinclair's  Locomotive-engine  Running  and  Management. 12 mo,  2  oo 

Smith's  (.O.)  Press-working  of  Metals 8vo,  3  oo 

Smith's  (A.  W.)  Materials  of  Machines I2mo,  i  oo 

Smith  (A.  W.)  and  Marx's  Machine  Design 8vo,  3  oo 

Spangler,  Greene,  and  Marshall's  Elements  of  Steam-engineering 8vo,  3  oo 

Thurston's  Treatise  on  Friction  and  Lost  Work  in    Machinery  and    Mill 

Work 8vo,  3  oo 

Animal  as  a  Machine  and  Prime  Motor,  and  the  Lawc  of  Energetics.  I2mo,  i  oo 

Tillson's  Complete  Automobile  Instructor i6mo,  i  50 

Morocco,  2  oo 

Warren's  Elements  of  Machine  Construction  and  Drawing 8vo,  7  So 

Weisbach's  Kinematics  and  Power  of  Transmission.   (Herrmann — Klein. ).8vo,  5  oo 

Machinery  of  Transmission  and  Governors.      (Herrmann — Klein. ).8vo,  5  oo 

Wood's  Elements  of  Analytical  Mechanics 8vo,  3  oo 

Principles  of  Elementary  Mechanics I2mo,  i  25 

Turbines 8TO,  2  50 

The  World's  Columbian  Exposition  of  1893 4to,  i  oo 

MEDICAL. 

De  Fursac's  Manual  of  Psychiatry.     (Rosanoff  and  Collins.) Large  I2mo,  2  50 

Ehrlich's  Collected  Studies  on  Immunity.     (Bolduan.) 8vo,    6  oo 

Hammarsten's  Text-book  on  Physiological  Chemistry.     (MandeL) 8vo,   4  oo 

16 


l/assar-Cobn's  Practical  Urinary  Analysis.     (Lorenz.) I2mo,  i  oo 

*  Pauli's  Physical  Chemistry  in  the  Service  of  Medicine.     (Fischer.).  ...  i2mo,  i   25 

*  Pozzi-Escot's  The  Toxins  and  Venoms  and  their  Antibodies.     (Cohn.).  izmo,  i  oo 

Rostoski's  Serum  Diagnosis.     (Bolduan.) 12010,  i  oo 

Salkowski's  Physiological  and  Pathological  Chemistry.     (Orndorff.) 8vo,  2  50 

*  Satterlee'*  Outlines  of  Human  Embryology I2mo,  i  25 

Steel's  Treatise  on  the  Diseases  of  the  Dog 8vo,  3  50 

Von  Behring's  Suppression  of  Tuberculosis.     (Bolduan.) 121110,  i  oo 

Wassermann's  Immune  Sera :  Haemolysis,  Cytotoxins,  and  Precipitins.     (Bol- 
duan.)   i2mo,  cloth,  i  oo 

Woodhull's  Notes  on  Military  Hygiene i6mo,  i  50 

*  Personal  Hygiene i2mo,  i  oo 

Wulling's  An  Elementary  Course  in  Inorganic  Pharmaceutical  and  Medical 

Chemistry 12010,  2  oo 

METALLURGY. 

Egleston's  Metallurgy  of  Silver,  Gold,  and  Mercury: 

Vol.    I.     Silver 8vo,  7  50 

Vol.  II.     Gold  and  Mercury 8vo,  7  50 

Goesel's  Minerals  and  Metals:     A  Reference  Book , . . .  .  i6mo,  mor.  3  oo 

*  Iles's  Lead-smelting 121110,  2  50 

Keep's  Cast  Iron 8vo,  2  50 

Kunhardt's  Practice  of  Ore  Dressing  in  Europe , 8vo,  i  50 

Le  Chatelier's  High-temperature  Measurements.  (Boudouard — Burgess. )i2mo,  3  oo 

Metcalf's  Steel.     A  Manual  for  Steel-users 12010,  2  oo 

Miller's  Cyanide  Process I2mo,  I  oo 

Minet's  Production  of  Aluminum  and  its  Industrial  Use.     (Waldo.). . .  .  12 mo,  2  50 

Robine  and  Lenglen's  Cyanide  Industry.     (Le  Clerc.) 8vo,  4  oo 

Smith's  Materials  of  Machines I2mo,  i  oo 

Thurston's  Materials  of  Engineering.     In  Three  Parts 8vo,  8  oo 

Part    II.     Iron  and  Steel 8vo,  3  50 

Part  HI.     A  Treatise  on  Brasses,  Bronzes,  and  Other  Alloys  and  their 

Constituents 8vo,  2  50 

Ulke's  Modern  Electrolytic  Copper  Refining 8vo,  3  oo 


MINERALOGY. 

Barringer's  Description  of  Minerals  of  Commercial  Value.    Oblong,  morocco,  2  50 

Boyd's  Resources  of  Southwest  Virginia 8vo,  3  oo 

Map  of  Southwest  Virignia Pocket-book  form.  2  oo 

*  Browning's  Introduction  to  the  Rarer  Elements 8vo,  150 

Brush's  Manual  of  Determinative  Mineralogy.     (Penfield.) 8vo,  4  oo 

Chester's  Catalogue  of  Minerals 8vo,  paper,  i  oo 

Cloth,  i  25 

Dictionary  of  the  Names  of  Minerals 8vo,  3  50 

Dana's  System  of  Mineralogy Large  8vo,  half  leather,  12  50 

First  Appendix  to  Dana's  New  "  System  of  Mineralogy." Large  8vo,  i  oo 

Text-book  of  Mineralogy 8vo,  4  oo 

Minerals  and  How  to  Study  Them I2mo,  i  50 

Catalogue  of  American  Localities  of  Minerals Large  8vo,  i  oo 

Manual  of  Mineralogy  and  Petrography izmo  2  oo 

Douglas's  Untechnical  Addresses  on  Technical  Subjects I2mo,  i  oo 

Eakle's  Mineral  Tables 8vo,  i  25 

Egleston's  Catalogue  of  Minerals  and  Synonyms 8vo,  2  50 

Goesel's  Minerals  and  Metals :     A  Reference  Book i6mo.mor.  300 

Groth's  Introduction  to  Chemical  Crystallography  (Marshall) 12 mo,  i  25 

17 


Iddings's  Rock  Minerals 8vo,  5  oo 

*  Martin's  Laboratory  Guide  to  Qualitative  Analysis  with  the  Blowpipe.  I2mo,  60 
Merrill's  Non-metallic  Minerals:  Their  Occurrence  and  Uses 8vo,  4  oo 

Stones  for  Building  and  Decoration 8vo,  5  oo 

*  Penfield's  Notes  on  Determinative  Mineralogy  and  Record  of  Mineral  Tests. 

8vo,  paper,  50 

*  Richards's  Synopsis  of  Mineral  Characters i2mo,  morocco,  i  25 

*  Ries's  Clays:  Their  Occurrence,  Properties,  and  Uses 8vo,  5  oo 

Rosenbusch's    Microscopical   Physiography   of   the    Rock-making  Minerals. 

(Iddings.) 8vo,  5  oo 

*  Tillman's  Text-book  of  Important  Minerals  and  Rocks 8vo,  2  oo 


MINING. 

Boyd's  Resources  of  Southwest  Virginia 8vo,  3  oo 

Map  of  Southwest  Virginia Pocket-book  form  2  oo 

Douglas's  Untechnical  Addresses  on  Technical  Subjects I2mo;  i  oo 

Eissler's  Modern  High  Explosives 873  4  ~>o 

ftoesel's  Minerals  and  Metals :     A  Reference  Book ibmo,  mor.  3  oo 

Goodyear's  Coal-mines  of  the  Western  Coa;t  of  the  United  States i2mo,  2  50 

Ihlseng's  Manual  of  Mining 8vo,  5  oo 

*  Iles's  Lead-smelting I2mo,  2  50 

Kunhardt's  Practice  of  Ore  Dressing  in  Europe 8vo,  i  50 

Miller's  Cyanide  Process I2mo,  i  oo 

O'Driscoll's  Notes  on  the  Treatment  of  Gold  Ores 8vo,  2  oo 

Robine  and  Lenglen's  Cyanide  Industry.     (Le  Clerc.) 8vo,  4  oo 

*  Walke's  Lectures  on  Explosives 8vo,  4  oo 

Weaver's  Military  Explosives 8vo,  3  oo 

Wilson's  Cyanide  Processes I2mo,  i  50 

Chlorination  Process i2mo,  i  50 

Hydraulic  and  Placer  Mining I2mo,  2  oo 

Treatise  on  Practical  and  Theoretical  Mine  Ventilation tamo,  i  25 


SANITARY  SCIENCE. 

Bashore's  Sanitation  of  a  Country  House I2mo,  i  oo 

*  Outlines  of  Practical  Sanitation I2mo,  i  25 

Folwell's  Sewerage.     (Designing,  Construction,  and  Maintenance.) 8vo,  3  oo 

Water-supply  Engineering 8vo,  4  oo 

Fowler's  Sewage  Works  Analyses 12013,  2  oo 

Fuertes's  Water  and  Public  Health I2mo,  i  50 

Water-filtration  Works I2mo,  2  50 

Gerhard's  Guide  to  Sanitary  House-inspection i6mo,  i  oo 

Hazen's  Filtration  of  Public  Water-supplies 8vo,  3  oo 

Leach's  The  Inspection  and  Analysis  of  Food  with  Special  Reference  to  State 

Control 8vo,  7  50 

Mason's  Water-supply.  (ConsideredprincipallyfromaSanitaryStandpoint)8vo,  4  oo 

Examination  of  Water.     (Chemical  and  Bacteriological) I2mo,  i  25 

*  Merriman's  Elements  of  Sanitary  Engineering 8vo,  2  oo 

Ogden's  Sewer  Design I2mo,  a  oo 

Prescott  and  Winslow's  Elements  of  Water  Bacteriology,  with  Special  Refer- 
ence to  Sanitary  Water  Analysis I2mo,  i  25 

*  Price's  Handbook  on  Sanitation 1 2 mo,  i  50 

Richards's  Cost  of  Food.     A  Study  in  Dietaries I2mo,  i  oo 

Cost  of  Living  as  Modified  by  Sanitary  Science i2mo,  i  oo 

Cost  of  Shelter i2mo,  i  oo 

18 


Richards   and   Woodman's  Air.   Water,  and  Food  from  a  Sanitary  Stand- 
point  8vo,  2  oo 

*  Richards  and  Williams's  The  Dietary  Computer 8vo,  i  50 

RideaPs  S  wage  and  Bacterial  Purification  of  Sewage 8vo,  4  oo 

Disinfection  and  the  Preservation  of  Food. 8vo,  4  oo 

Turneaure  and  Russell's  Public  Water-supplies 8vo,  5  oo 

Von  Behring's  Suppression  of  Tuberculosis.     (Bolduan.) 121110,  i  oo 

Whipple's  Microscopy  of  Drinking-water 8vo,  3  50 

Winton's  Microscopy  of  Vegetable  Foods 8vo,  7  50 

Woodhull's  Notes  on  Military  Hygiene ; i6mo,  i  50 

*  Personal  Hygiene i2mo,  i  oo 


MISCELLANEOUS. 

Emmons's  Geological  Guide-book  of  the  Rocky  Mountain  Excursion  of  the 

International  Congress  of  Geologists Large  Svo,  i  50 

Ferrel's  Popular  Treatise  on  the  Winds 8vo,  4  oo 

Gannett's  Statistical  Abstract  of  the  World 24010 ,  75 

Haines's  American  Railway  Management I2mo,  2  50 

Ricketts's  History  of  Rensselaer  Polytechnic  Institute,  1824-1894.  .Small  Svo,  3  oo 

Rotherham's  Emphasized  Hew  Teftament c Large  Svo,  2  oc 

The  World's  Columbian  Exposition  of  1893 4to,  i  oc 

Winslow's  Elements  of  Applied  Microscopy I2mo,  i  50 


HEBREW  AND   CHALDEE  TEXT-BOOKS. 

Green's  Elementary  Hebrew  Grammar I2mo,  I  25 

Hebrew  Chrestomathy 8vo,  2  oo 

Gesenius's  Hebrew  and  Chaldee  Lexicon  to  the  Old  Testament  Scriptures. 

(Tregelles.) Small  4to,  half  morocco,  5  oo 

Letteris's  Hebrew  Bible , Svo,  2  25 

19 


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